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Chapters
2: Functions
3: Binary Operations
4: Inverse Trigonometric Functions
5: Algebra of Matrices
6: Determinants
▶ 7: Adjoint and Inverse of a Matrix
8: Solution of Simultaneous Linear Equations
9: Continuity
10: Differentiability
11: Differentiation
12: Higher Order Derivatives
13: Derivative as a Rate Measurer
14: Differentials, Errors and Approximations
15: Mean Value Theorems
16: Tangents and Normals
17: Increasing and Decreasing Functions
18: Maxima and Minima
19: Indefinite Integrals
20: Definite Integrals
21: Areas of Bounded Regions
22: Differential Equations
23: Algebra of Vectors
24: Scalar Or Dot Product
25: Vector or Cross Product
26: Scalar Triple Product
27: Direction Cosines and Direction Ratios
28: Straight Line in Space
29: The Plane
30: Linear programming
31: Probability
32: Mean and Variance of a Random Variable
33: Binomial Distribution
![RD Sharma solutions for Mathematics [English] Class 12 chapter 7 - Adjoint and Inverse of a Matrix - Shaalaa.com](/images/mathematics-english-class-12_6:be05c27f33094688837f0fdb2cb69ac3.jpg "RD Sharma solutions for Mathematics [English] Class 12 chapter 7 - Adjoint and Inverse of a Matrix")
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Solutions for Chapter 7: Adjoint and Inverse of a Matrix
Below listed, you can find solutions for Chapter 7 of CBSE, Karnataka Board PUC RD Sharma for Mathematics [English] Class 12.
RD Sharma solutions for Mathematics [English] Class 12 7 Adjoint and Inverse of a Matrix Exercise 7.1 [Pages 22 - 25]
Find the adjoint of the following matrix:
\[\begin{bmatrix}- 3 & 5 \\ 2 & 4\end{bmatrix}\]
Find the adjoint of the following matrix:
\[\begin{bmatrix}a & b \\ c & d\end{bmatrix}\]
Find the adjoint of the following matrix:
\[\begin{bmatrix}\cos \alpha & \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\]
Find the adjoint of the following matrix:
Verify that (adj A) A = |A| I = A (adj A) for the above matrix.
Compute the adjoint of the following matrix:
\[\begin{bmatrix}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{bmatrix}\]
Verify that (adj A) A = |A| I = A (adj A) for the above matrix.
Compute the adjoint of the following matrix:
Verify that (adj A) A = |A| I = A (adj A) for the above matrix.
Compute the adjoint of the following matrix:
Verify that (adj A) A = |A| I = A (adj A) for the above matrix.
Compute the adjoint of the following matrix:
Verify that (adj A) A = |A| I = A (adj A) for the above matrix.
For the matrix
If \[A = \begin{bmatrix}- 4 & - 3 & - 3 \\ 1 & 0 & 1 \\ 4 & 4 & 3\end{bmatrix}\], show that adj A = A.
If \[A = \begin{bmatrix}- 1 & - 2 & - 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1\end{bmatrix}\] , show that adj A = 3AT.
Find A (adj A) for the matrix \[A = \begin{bmatrix}1 & - 2 & 3 \\ 0 & 2 & - 1 \\ - 4 & 5 & 2\end{bmatrix} .\]
Find the inverse of the following matrix:
Find the inverse of the following matrix:
Find the inverse of the following matrix:
Find the inverse of the following matrix:
Find the inverse of the following matrix.
\[\begin{bmatrix}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{bmatrix}\]
Find the inverse of the following matrix.
Find the inverse of the following matrix.
Find the inverse of the following matrix.
Find the inverse of the following matrix.
Find the inverse of the following matrix.
Find the inverse of the following matrix.
Find the inverse of the following matrix and verify that \[A^{- 1} A = I_3\]
Find the inverse of the following matrix and verify that \[A^{- 1} A = I_3\]
For the following pair of matrix verify that \[\left( AB \right)^{- 1} = B^{- 1} A^{- 1} :\]
\[A = \begin{bmatrix}3 & 2 \\ 7 & 5\end{bmatrix}\text{ and }B \begin{bmatrix}4 & 6 \\ 3 & 2\end{bmatrix}\]
For the following pair of matrix verify that \[\left( AB \right)^{- 1} = B^{- 1} A^{- 1} :\]
\[A = \begin{bmatrix}2 & 1 \\ 5 & 3\end{bmatrix}\text{ and }B \begin{bmatrix}4 & 5 \\ 3 & 4\end{bmatrix}\]
Let \[A = \begin{bmatrix}3 & 2 \\ 7 & 5\end{bmatrix}\text{ and }B = \begin{bmatrix}6 & 7 \\ 8 & 9\end{bmatrix} .\text{ Find }\left( AB \right)^{- 1}\]
Given \[A = \begin{bmatrix}2 & - 3 \\ - 4 & 7\end{bmatrix}\], compute A−1 and show that \[2 A^{- 1} = 9I - A .\]
If \[A = \begin{bmatrix}4 & 5 \\ 2 & 1\end{bmatrix}\] , then show that \[A - 3I = 2 \left( I + 3 A^{- 1} \right) .\]
Find the inverse of the matrix \[A = \begin{bmatrix}a & b \\ c & \frac{1 + bc}{a}\end{bmatrix}\] and show that \[a A^{- 1} = \left( a^2 + bc + 1 \right) I - aA .\]
Given \[A = \begin{bmatrix}5 & 0 & 4 \\ 2 & 3 & 2 \\ 1 & 2 & 1\end{bmatrix}, B^{- 1} = \begin{bmatrix}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\] . Compute (AB)−1.
Let
\[F \left( \alpha \right) = \begin{bmatrix}\cos \alpha & - \sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{bmatrix}\text{ and }G\left( \beta \right) = \begin{bmatrix}\cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ - \sin \beta & 0 & \cos \beta\end{bmatrix}\]
Show that
If \[A = \begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix}\] , verify that \[A^2 - 4 A + I = O,\text{ where }I = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\text{ and }O = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}\] . Hence, find A−1.
Show that
If \[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix}\], show that
If \[A = \begin{bmatrix}4 & 3 \\ 2 & 5\end{bmatrix}\], find x and y such that
If \[A = \begin{bmatrix}3 & - 2 \\ 4 & - 2\end{bmatrix}\], find the value of \[\lambda\] so that \[A^2 = \lambda A - 2I\]. Hence, find A−1.
Show that \[A = \begin{bmatrix}5 & 3 \\ - 1 & - 2\end{bmatrix}\] satisfies the equation \[x^2 - 3x - 7 = 0\]. Thus, find A−1.
Show that \[A = \begin{bmatrix}6 & 5 \\ 7 & 6\end{bmatrix}\] satisfies the equation \[x^2 - 12x + 1 = O\]. Thus, find A−1.
For the matrix \[A = \begin{bmatrix}1 & 1 & 1 \\ 1 & 2 & - 3 \\ 2 & - 1 & 3\end{bmatrix}\] . Show that
Show that the matrix, \[A = \begin{bmatrix}1 & 0 & - 2 \\ - 2 & - 1 & 2 \\ 3 & 4 & 1\end{bmatrix}\] satisfies the equation, \[A^3 - A^2 - 3A - I_3 = O\] . Hence, find A−1.
Verify that \[A^3 - 6 A^2 + 9A - 4I = O\] and hence find A−1.
prove that \[A^{- 1} = A^3\]
If \[A = \begin{bmatrix}3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1\end{bmatrix}\] , show that \[A^{- 1} = A^3\]
If \[A = \begin{bmatrix}- 1 & 2 & 0 \\ - 1 & 1 & 1 \\ 0 & 1 & 0\end{bmatrix}\] , show that \[A^2 = A^{- 1} .\]
Solve the matrix equation \[\begin{bmatrix}5 & 4 \\ 1 & 1\end{bmatrix}X = \begin{bmatrix}1 & - 2 \\ 1 & 3\end{bmatrix}\], where X is a 2 × 2 matrix.
Find the matrix X satisfying the matrix equation \[X\begin{bmatrix}5 & 3 \\ - 1 & - 2\end{bmatrix} = \begin{bmatrix}14 & 7 \\ 7 & 7\end{bmatrix}\]
Find the matrix X for which
Find the matrix X satisfying the equation
If \[A = \begin{bmatrix}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{bmatrix}\] , find \[A^{- 1}\] and prove that \[A^2 - 4A - 5I = O\]
If \[A = \begin{bmatrix}1 & - 2 & 3 \\ 0 & - 1 & 4 \\ - 2 & 2 & 1\end{bmatrix},\text{ find }\left( A^T \right)^{- 1} .\]
Find the adjoint of the matrix \[A = \begin{bmatrix}- 1 & - 2 & - 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1\end{bmatrix}\] and hence show that \[A\left( adj A \right) = \left| A \right| I_3\].
RD Sharma solutions for Mathematics [English] Class 12 7 Adjoint and Inverse of a Matrix Exercise 7.2 [Page 34]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}7 & 1 \\ 4 & - 3\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}5 & 2 \\ 2 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}1 & 6 \\ - 3 & 5\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}3 & 10 \\ 2 & 7\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}2 & 0 & - 1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}2 & 3 & 1 \\ 2 & 4 & 1 \\ 3 & 7 & 2\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}1 & 2 & 0 \\ 2 & 3 & - 1 \\ 1 & - 1 & 3\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}2 & - 1 & 3 \\ 1 & 2 & 4 \\ 3 & 1 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}1 & 1 & 2 \\ 3 & 1 & 1 \\ 2 & 3 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}2 & - 1 & 4 \\ 4 & 0 & 7 \\ 3 & - 2 & 7\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}3 & 0 & - 1 \\ 2 & 3 & 0 \\ 0 & 4 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}1 & 3 & - 2 \\ - 3 & 0 & - 1 \\ 2 & 1 & 0\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}- 1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{bmatrix}\]
RD Sharma solutions for Mathematics [English] Class 12 7 Adjoint and Inverse of a Matrix Exercise 7.3 [Pages 35 - 36]
Write the adjoint of the matrix \[A = \begin{bmatrix}- 3 & 4 \\ 7 & - 2\end{bmatrix} .\]
If A is a square matrix such that A (adj A) 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.
If A is a square matrix of order 3 such that |A| = 5, write the value of |adj A|.
If A is a square matrix of order 3 such that |adj A| = 64, find |A|.
If A is a non-singular square matrix such that |A| = 10, find |A−1|.
If A, B, C are three non-null square matrices of the same order, write the condition on A such that AB = AC⇒ B = C.
If A is a non-singular square matrix such that \[A^{- 1} = \begin{bmatrix}5 & 3 \\ - 2 & - 1\end{bmatrix}\] , then find \[\left( A^T \right)^{- 1} .\]
If adj \[A = \begin{bmatrix}2 & 3 \\ 4 & - 1\end{bmatrix}\text{ and adj }B = \begin{bmatrix}1 & - 2 \\ - 3 & 1\end{bmatrix}\]
If A is symmetric matrix, write whether AT is symmetric or skew-symmetric.
If A is a square matrix of order 3 such that |A| = 2, then write the value of adj (adj A).
If A is a square matrix of order 3 such that |A| = 3, then write the value of adj (adj A).
If A is a square matrix of order 3 such that adj (2A) = k adj (A), then write the value of k.
If A is a square matrix, then write the matrix adj (AT) − (adj A)T.
Let A be a 3 × 3 square matrix, such that A (adj A) = 2 I, where I is the identity matrix. Write the value of |adj A|.
If A is a non-singular symmetric matrix, write whether A−1 is symmetric or skew-symmetric.
If \[A = \begin{bmatrix}\cos \theta & \sin \theta \\ - \sin \theta & \cos \theta\end{bmatrix}\text{ and }A \left( adj A = \right)\begin{bmatrix}k & 0 \\ 0 & k\end{bmatrix}\], then find the value of k.
If A is an invertible matrix such that |A−1| = 2, find the value of |A|.
If A is a square matrix such that \[A \left( adj A \right) = \begin{bmatrix}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{bmatrix}\] , then write the value of |adj A|.
If \[A = \begin{bmatrix}2 & 3 \\ 5 & - 2\end{bmatrix}\] be such that \[A^{- 1} = k A,\] then find the value of k.
Let A be a square matrix such that \[A^2 - A + I = O\], then write \[A^{- 1}\] interms of A.
If Cij is the cofactor of the element aij of the matrix \[A = \begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix}\], then write the value of a32C32.
Find the inverse of the matrix \[\begin{bmatrix}3 & - 2 \\ - 7 & 5\end{bmatrix} .\]
Find the inverse of the matrix \[\begin{bmatrix} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta\end{bmatrix}\]
If \[A = \begin{bmatrix}1 & - 3 \\ 2 & 0\end{bmatrix}\], write adj A.
If \[A = \begin{bmatrix}a & b \\ c & d\end{bmatrix}, B = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\] , find adj (AB).
If \[A = \begin{bmatrix}3 & 1 \\ 2 & - 3\end{bmatrix}\], then find |adj A|.
If \[A = \begin{bmatrix}2 & 3 \\ 5 & - 2\end{bmatrix}\] , write \[A^{- 1}\] in terms of A.
Write \[A^{- 1}\text{ for }A = \begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation : \[\begin{bmatrix} 2 & 1 \\ 2 & 0\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 1 & 1\end{bmatrix}\]
In the following matrix equation use elementary operation R2 → R2 + R1 and the equation thus obtained:
RD Sharma solutions for Mathematics [English] Class 12 7 Adjoint and Inverse of a Matrix Exercise 7.4 [Pages 37 - 39]
If A is an invertible matrix, then which of the following is not true ?
\[\left( A^2 \right)^{- 1} = \left( A^{- 1} \right)^2\]
\[\left| A^{- 1} \right| = \left| A \right|^{- 1}\]
\[\left( A^T \right)^{- 1} = \left( A^{- 1} \right)^T\]
\[\left| A \right| \neq 0\]
If A is an invertible matrix of order 3, then which of the following is not true ?
\[\left| adj A \right| = \left| A \right|^2\]
\[\left( A^{- 1} \right)^{- 1} = A\]
If \[BA = CA,\text{ than }B \neq C\] , where B and C are square matrices of order 3
\[\left( AB \right)^{- 1} = B^{- 1} A^{- 1} , where B \neq \left[ b_{ij} \right]_{3 \times 3} and \left| B \right| \neq 0\]
If \[A = \begin{bmatrix}3 & 4 \\ 2 & 4\end{bmatrix}, B = \begin{bmatrix}- 2 & - 2 \\ 0 & - 1\end{bmatrix},\text{ then }\left( A + B \right)^{- 1} =\]
is a skew-symmetric matrix
A−1 + B−1
does not exist
none of these
If \[S = \begin{bmatrix}a & b \\ c & d\end{bmatrix}\], then adj A is ____________ .
\[\begin{bmatrix}- d & - b \\ - c & a\end{bmatrix}\]
\[\begin{bmatrix}d & - b \\ - c & a\end{bmatrix}\]
\[\begin{bmatrix}d & b \\ c & a\end{bmatrix}\]
\[\begin{bmatrix}d & c \\ b & a\end{bmatrix}\]
If A is a singular matrix, then adj A is ______.
non-singular
singular
symmetric
not defined
If A, B are two n × n non-singular matrices, then __________ .
AB is non-singular
AB is singular
\[\left( AB \right)^{- 1} A^{- 1} B^{- 1}\]
(AB)−1 does not exist
If \[A = \begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{bmatrix}\] , then the value of |adj A| is _____________ .
a27
a9
a6
a2
If \[A = \begin{bmatrix}1 & 2 & - 1 \\ - 1 & 1 & 2 \\ 2 & - 1 & 1\end{bmatrix}\] , then ded (adj (adj A)) is __________ .
144
143
142
14
If B is a non-singular matrix and A is a square matrix, then det (B−1 AB) is equal to ___________ .
Det (A−1)
Det (B−1)
Det (A)
Det (B)
For any 2 × 2 matrix, if \[A \left( adj A \right) = \begin{bmatrix}10 & 0 \\ 0 & 10\end{bmatrix}\] , then |A| is equal to ______ .
20
100
10
0
If A5 = O such that \[A^n \neq I\text{ for }1 \leq n \leq 4,\text{ then }\left( I - A \right)^{- 1}\] equals ________ .
A4
A3
I + A
none of these
If A satisfies the equation \[x^3 - 5 x^2 + 4x + \lambda = 0\] then A-1 exists if _____________ .
\[\lambda = 1\]
\[\lambda \neq 2\]
\[\lambda \neq -1\]
\[\lambda \neq 0\]
If for the matrix A, A3 = I, then A−1 = _____________ .
A2
A3
A
none of these
If A and B are square matrices such that B = − A−1 BA, then (A + B)2 = ________ .
O
A2 + B2
A2 + 2AB + B2
A + B
If \[A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{bmatrix},\text{ then }A^5 =\] ____________ .
5A
10A
16A
32A
For non-singular square matrix A, B and C of the same order \[\left( A B^{- 1} C \right) =\] ______________ .
\[A^{- 1} B C^{- 1}\]
\[C^{- 1} B^{- 1} A^{- 1}\]
\[CB A^{- 1}\]
\[C^{- 1} BA^{- 1}\]
The matrix \[\begin{bmatrix}5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b\end{bmatrix}\] is a singular matrix, if the value of b is _____________ .
-3
3
0
non-existent
If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is _____________ .
dn
dn−1
dn+1
d
If A is a matrix of order 3 and |A| = 8, then |adj A| = __________ .
1
2
23
26
If \[A^2 - A + I = 0\], then the inverse of A is __________ .
A−2
A + I
I − A
A − I
If A and B are invertible matrices, which of the following statement is not correct.
\[adj A = \left| A \right| A^{- 1}\]
\[\det \left( A^{- 1} \right) = \left( \det A \right)^{- 1}\]
\[\left( A + B \right)^{- 1} = A^{- 1} + B^{- 1}\]
\[\left( AB \right)^{- 1} = B^{- 1} A^{- 1}\]
If A is a square matrix such that A2 = I, then A−1 is equal to _______ .
A + I
A
0
2A
Let \[A = \begin{bmatrix}1 & 2 \\ 3 & - 5\end{bmatrix}\text{ and }B = \begin{bmatrix}1 & 0 \\ 0 & 2\end{bmatrix}\] and X be a matrix such that A = BX, then X is equal to _____________ .
\[\frac{1}{2}\begin{bmatrix}2 & 4 \\ 3 & - 5\end{bmatrix}\]
\[\frac{1}{2}\begin{bmatrix}- 2 & 4 \\ 3 & 5\end{bmatrix}\]
\[\begin{bmatrix}2 & 4 \\ 3 & - 5\end{bmatrix}\]
none of these
If \[A = \begin{bmatrix}2 & 3 \\ 5 & - 2\end{bmatrix}\] be such that \[A^{- 1} = kA\], then k equals ___________ .
19
`1/19`
-19
`-1/19`
(a) 3
(b) 0
(c) − 3
(d) 1
3
0
-3
1
None of these
If \[A = \begin{bmatrix}1 & 0 & 1 \\ 0 & 0 & 1 \\ a & b & 2\end{bmatrix},\text{ then aI + bA + 2 }A^2\] equals ____________ .
A
-A
ab A
none of these
If \[\begin{bmatrix}1 & - \tan \theta \\ \tan \theta & 1\end{bmatrix} \begin{bmatrix}1 & \tan \theta \\ - \tan \theta & 1\end{bmatrix} - 1 = \begin{bmatrix}a & - b \\ b & a\end{bmatrix}\], then _______________ .
\[a = 1, b = 1\]
\[a = \cos 2 \theta, b = \sin 2 \theta\]
\[a = \sin 2 \theta, b = \cos 2 \theta\]
None of these
If a matrix A is such that \[3A^3 + 2 A^2 + 5 A + I = 0,\text{ then }A^{- 1}\] equal to _______________ .
\[- \left( 3 A^2 + 2 A + 5 \right)\]
\[3 A^2 + 2 A + 5\]
\[3 A^2 - 2 A - 5\]
none of these
If A is an invertible matrix, then det (A−1) is equal to ____________ .
det (A)
\[\frac{1}{det \left( A \right)}\]
1
none of these
\[A^n = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\], if n is an even natural number
\[A^n = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\] , if n is an odd natural number
\[A^n = \begin{bmatrix}- 1 & 0 \\ 0 & 1\end{bmatrix}\], if n ∈ N
none of these
\[\begin{bmatrix}x^{- 1} & 0 & 0 \\ 0 & y^{- 1} & 0 \\ 0 & 0 & z^{- 1}\end{bmatrix}\]
\[xyz \begin{bmatrix}x^{- 1} & 0 & 0 \\ 0 & y^{- 1} & 0 \\ 0 & 0 & z^{- 1}\end{bmatrix}\]
\[\frac{1}{xyz}\begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}\]
\[\frac{1}{xyz} \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\]
Solutions for 7: Adjoint and Inverse of a Matrix
RD Sharma solutions for Mathematics [English] Class 12 chapter 7 - Adjoint and Inverse of a Matrix
Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Mathematics [English] Class 12 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Mathematics [English] Class 12 CBSE, Karnataka Board PUC 7 (Adjoint and Inverse of a Matrix) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Mathematics [English] Class 12 chapter 7 Adjoint and Inverse of a Matrix are Applications of Determinants and Matrices, Determinant of a Matrix, Expansion of Determinant, Area of Triangle using Determinant, Minors and Co-factors, Overview of Determinants, Adjoint & Inverse of Matrix.
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