English

If A = [01312x231], A–1 = [12-452-123-3212y12] then x = 1, y = –1. - Mathematics

Advertisements
Advertisements

Question

If A = `[(0, 1, 3),(1, 2, x),(2, 3, 1)]`, A–1 = `[(1/2, -4, 5/2),(-1/2, 3, -3/2),(1/2, y, 1/2)]` then x = 1, y = –1.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is True.

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Determinants - Solved Examples [Page 77]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 4 Determinants
Solved Examples | Q 18 | Page 77

RELATED QUESTIONS

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. School A wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively with a total award money of Rs 1,600. School B wants to spend Rs 2,300 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for an award.


Find the adjoint of the matrices.

`[(1,-1,2),(2,3,5),(-2,0,1)]`


Find the inverse of the matrices (if it exists).

`[(2,1,3),(4,-1,0),(-7,2,1)]`


For the matrix A = `[(1,1,1),(1,2,-3),(2,-1,3)]` show that A3 − 6A2 + 5A + 11 I = 0. Hence, find A−1.


If A = `[(2,-1,1),(-1,2,-1),(1,-1,2)]` verify that A3 − 6A2 + 9A − 4I = 0 and hence find A−1.


If A−1 = `[(3,-1,1),(-15,6,-5),(5,-2,2)]` and B = `[(1,2,-2),(-1,3,0),(0,-2,1)]`, find (AB)−1.


Let A = `[(1, sin theta, 1),(-sin theta,1,sin theta),(-1, -sin theta, 1)]` where 0 ≤ θ ≤ 2π, then ______.


Find the adjoint of the following matrix:
\[\begin{bmatrix}\cos \alpha & \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\]

Verify that (adj A) A = |A| I = A (adj A) for the above matrix.

Compute the adjoint of the following matrix:

\[\begin{bmatrix}2 & - 1 & 3 \\ 4 & 2 & 5 \\ 0 & 4 & - 1\end{bmatrix}\]

Verify that (adj A) A = |A| I = A (adj A) for the above matrix.


Find the inverse of the following matrix:

\[\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\]

Find the inverse of the following matrix.

\[\begin{bmatrix}1 & 2 & 5 \\ 1 & - 1 & - 1 \\ 2 & 3 & - 1\end{bmatrix}\]

Find the inverse of the following matrix and verify that \[A^{- 1} A = I_3\]

\[\begin{bmatrix}2 & 3 & 1 \\ 3 & 4 & 1 \\ 3 & 7 & 2\end{bmatrix}\]

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 \[A = \begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix}\] , 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

\[A = \begin{bmatrix}- 8 & 5 \\ 2 & 4\end{bmatrix}\] satisfies the equation \[A^2 + 4A - 42I = O\]. Hence, 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.


If \[A = \begin{bmatrix}2 & - 1 & 1 \\ - 1 & 2 & - 1 \\ 1 & - 1 & 2\end{bmatrix}\].
Verify that \[A^3 - 6 A^2 + 9A - 4I = O\]  and hence find A−1.

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 inverse by using elementary row transformations:

\[\begin{bmatrix}7 & 1 \\ 4 & - 3\end{bmatrix}\]


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:

\[\begin{bmatrix}1 & 1 & 2 \\ 3 & 1 & 1 \\ 2 & 3 & 1\end{bmatrix}\]


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:

\[\begin{bmatrix}1 & 3 & - 2 \\ - 3 & 0 & - 1 \\ 2 & 1 & 0\end{bmatrix}\]


If A is a non-singular symmetric matrix, write whether A−1 is symmetric or skew-symmetric.


If A is an invertible matrix such that |A−1| = 2, find the value of |A|.


If A is an invertible matrix of order 3, then which of the following is not true ?


If A satisfies the equation \[x^3 - 5 x^2 + 4x + \lambda = 0\] then A-1 exists if _____________ .


If x, y, z are non-zero real numbers, then the inverse of the matrix \[A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}\], is _____________ .

(A3)–1 = (A–1)3, where A is a square matrix and |A| ≠ 0.


|A–1| ≠ |A|–1, where A is non-singular matrix.


Find the adjoint of the matrix A `= [(1,2),(3,4)].`


For what value of x, matrix `[(6-"x", 4),(3-"x", 1)]` is a singular matrix?


The value of `abs (("cos" (alpha + beta),-"sin" (alpha + beta),"cos"  2 beta),("sin" alpha, "cos" alpha, "sin" beta),(-"cos" alpha, "sin" alpha, "cos" beta))` is independent of ____________.


If `abs((2"x", -1),(4,2)) = abs ((3,0),(2,1))` then x is ____________.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×