Advertisements
Advertisements
प्रश्न
Find the inverse of the following matrix.
Advertisements
उत्तर
\[B = \begin{bmatrix}1 & 2 & 5 \\ 1 & - 1 & - 1 \\ 2 & 3 & - 1\end{bmatrix}\]
Now,
\[ C_{11} = \begin{vmatrix}- 1 & - 1 \\ 3 & - 1\end{vmatrix} = 4, C_{12} = - \begin{vmatrix}1 & - 1 \\ 2 & - 1\end{vmatrix} = - 1\text{ and }C_{13} = \begin{vmatrix}1 & - 1 \\ 2 & 3\end{vmatrix} = 5\]
\[ C_{21} = - \begin{vmatrix}2 & 5 \\ 3 & - 1\end{vmatrix} = 17, C_{22} = \begin{vmatrix}1 & 5 \\ 2 & - 1\end{vmatrix} = - 11\text{ and }C_{23} = - \begin{vmatrix}1 & 2 \\ 2 & 3\end{vmatrix} = 1\]
\[ C_{31} = \begin{vmatrix}2 & 5 \\ - 1 & - 1\end{vmatrix} = 3, C_{32} = - \begin{vmatrix}1 & 5 \\ 1 & - 1\end{vmatrix} = 6\text{ and }C_{33} = \begin{vmatrix}1 & 2 \\ 1 & - 1\end{vmatrix} = - 3\]
\[adjB = \begin{bmatrix}4 & - 1 & 5 \\ 17 & - 11 & 1 \\ 3 & 6 & - 3\end{bmatrix}^T = \begin{bmatrix}4 & 17 & 3 \\ - 1 & - 11 & 6 \\ 5 & 1 & - 3\end{bmatrix}\]
\[\text{ and }\left| B \right| = 27\]
\[ \therefore B^{- 1} = \frac{1}{27}\begin{bmatrix}4 & 17 & 3 \\ - 1 & - 11 & 6 \\ 5 & 1 & - 3\end{bmatrix}\]
APPEARS IN
संबंधित प्रश्न
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 inverse of the matrices (if it exists).
`[(1,0,0),(0, cos alpha, sin alpha),(0, sin alpha, -cos alpha)]`
Let A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`. Verify that (AB)−1 = B−1A−1.
For the matrix A = `[(3,2),(1,1)]` find the numbers a and b such that A2 + aA + bI = 0.
If A is an invertible matrix of order 2, then det (A−1) is equal to ______.
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
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 \[A^{- 1} A = I_3\]
For the matrix \[A = \begin{bmatrix}1 & 1 & 1 \\ 1 & 2 & - 3 \\ 2 & - 1 & 3\end{bmatrix}\] . Show that
prove that \[A^{- 1} = A^3\]
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
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}7 & 1 \\ 4 & - 3\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{bmatrix}\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}2 & 0 & - 1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{bmatrix}\]
If adj \[A = \begin{bmatrix}2 & 3 \\ 4 & - 1\end{bmatrix}\text{ and adj }B = \begin{bmatrix}1 & - 2 \\ - 3 & 1\end{bmatrix}\]
If \[A = \begin{bmatrix}\cos \theta & \sin \theta \\ - \sin \theta & \cos \theta\end{bmatrix}\text{ and }A \left( adj A = \right)\begin{bmatrix}k & 0 \\ 0 & k\end{bmatrix}\], then find the value of k.
If A is an invertible matrix, then which of the following is not true ?
If A, B are two n × n non-singular matrices, then __________ .
If B is a non-singular matrix and A is a square matrix, then det (B−1 AB) is equal to ___________ .
If A5 = O such that \[A^n \neq I\text{ for }1 \leq n \leq 4,\text{ then }\left( I - A \right)^{- 1}\] equals ________ .
If A satisfies the equation \[x^3 - 5 x^2 + 4x + \lambda = 0\] then A-1 exists if _____________ .
If A = `[(x, 5, 2),(2, y, 3),(1, 1, z)]`, xyz = 80, 3x + 2y + 10z = 20, ten A adj. A = `[(81, 0, 0),(0, 81, 0),(0, 0, 81)]`
If A and B are invertible matrices, then which of the following is not correct?
`("aA")^-1 = 1/"a" "A"^-1`, where a is any real number and A is a square matrix.
|A–1| ≠ |A|–1, where A is non-singular matrix.
Find the adjoint of the matrix A `= [(1,2),(3,4)].`
Find x, if `[(1,2,"x"),(1,1,1),(2,1,-1)]` is singular
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 ____________.
For matrix A = `[(2,5),(-11,7)]` (adj A)' is equal to:
Read the following passage:
|
Gautam buys 5 pens, 3 bags and 1 instrument box and pays a sum of ₹160. From the same shop, Vikram buys 2 pens, 1 bag and 3 instrument boxes and pays a sum of ₹190. Also, Ankur buys 1 pen, 2 bags and 4 instrument boxes and pays a sum of ₹250. |
Based on the above information, answer the following questions:
- Convert the given above situation into a matrix equation of the form AX = B. (1)
- Find | A |. (1)
- Find A–1. (2)
OR
Determine P = A2 – 5A. (2)
