Advertisements
Advertisements
प्रश्न
Find the inverse of the following matrix.
Advertisements
उत्तर
\[F = \begin{bmatrix}0 & 0 & - 1 \\ 3 & 4 & 5 \\ - 2 & - 4 & - 7\end{bmatrix}\]
Now,
\[ C_{11} = \begin{vmatrix}4 & 5 \\ - 4 & - 7\end{vmatrix} = - 8, C_{12} = - \begin{vmatrix}3 & 5 \\ - 2 & - 7\end{vmatrix} = 11\text{ and }C_{13} = \begin{vmatrix}3 & 4 \\ - 2 & - 4\end{vmatrix} = - 4\]
\[ C_{21} = - \begin{vmatrix}0 & - 1 \\ - 4 & - 7\end{vmatrix} = 4, C_{22} = \begin{vmatrix}0 & - 1 \\ - 2 & - 7\end{vmatrix} = - 2\text{ and }C_{23} = - \begin{vmatrix}0 & 0 \\ - 2 & - 4\end{vmatrix} = 0\]
\[ C_{31} = \begin{vmatrix}0 & - 1 \\ 4 & 5\end{vmatrix} = 4, C_{32} = - \begin{vmatrix}0 & - 1 \\ 3 & 5\end{vmatrix} = - 3\text{ and }C_{33} = \begin{vmatrix}0 & 0 \\ 3 & 4\end{vmatrix} = 0\]
\[adjF = \begin{bmatrix}- 8 & 11 & - 4 \\ 4 & - 2 & 0 \\ 4 & - 3 & 0\end{bmatrix}^T = \begin{bmatrix}- 8 & 4 & 4 \\ 11 & - 2 & - 3 \\ - 4 & 0 & 0\end{bmatrix}\]
\[\text{ and }\left| F \right| = 4\]
\[ \therefore F^{- 1} = \frac{1}{4}\begin{bmatrix}- 8 & 4 & 4 \\ 11 & - 2 & - 3 \\ - 4 & 0 & 0\end{bmatrix}\]
APPEARS IN
संबंधित प्रश्न
Find the adjoint of the matrices.
`[(1,-1,2),(2,3,5),(-2,0,1)]`
If A is an invertible matrix of order 2, then det (A−1) is equal to ______.
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.
If x, y, z are nonzero real numbers, then the inverse of matrix A = `[(x,0,0),(0,y,0),(0,0,z)]` is ______.
Let A = `[(1, sin theta, 1),(-sin theta,1,sin theta),(-1, -sin theta, 1)]` where 0 ≤ θ ≤ 2π, then ______.
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.
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 \[A^{- 1} A = I_3\]
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.
If \[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix}\], show 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.
If \[A = \begin{bmatrix}- 1 & 2 & 0 \\ - 1 & 1 & 1 \\ 0 & 1 & 0\end{bmatrix}\] , show that \[A^2 = A^{- 1} .\]
Find the inverse by using elementary row transformations:
\[\begin{bmatrix}1 & 3 & - 2 \\ - 3 & 0 & - 1 \\ 2 & 1 & 0\end{bmatrix}\]
If A is symmetric matrix, write whether AT is symmetric or skew-symmetric.
If \[A = \begin{bmatrix}1 & - 3 \\ 2 & 0\end{bmatrix}\], write adj A.
If \[A = \begin{bmatrix}3 & 4 \\ 2 & 4\end{bmatrix}, B = \begin{bmatrix}- 2 & - 2 \\ 0 & - 1\end{bmatrix},\text{ then }\left( A + B \right)^{- 1} =\]
If \[A = \begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{bmatrix}\] , then the value of |adj A| is _____________ .
If for the matrix A, A3 = I, then A−1 = _____________ .
If A is an invertible matrix, then det (A−1) is equal to ____________ .
If A and B are invertible matrices, then which of the following is not correct?
If A, B be two square matrices such that |AB| = O, then ____________.
A square matrix A is invertible if det A is equal to ____________.
Find the adjoint of the matrix A `= [(1,2),(3,4)].`
Find the value of x for which the matrix A `= [(3 - "x", 2, 2),(2,4 - "x", 1),(-2,- 4,-1 - "x")]` is singular.
If A = [aij] is a square matrix of order 2 such that aij = `{(1"," "when i" ≠ "j"),(0"," "when" "i" = "j"):},` then A2 is ______.
A and B are invertible matrices of the same order such that |(AB)-1| = 8, If |A| = 2, then |B| is ____________.
If A is a square matrix of order 3 and |A| = 5, then |adj A| = ______.
If A = `[(1/sqrt(5), 2/sqrt(5)),((-2)/sqrt(5), 1/sqrt(5))]`, B = `[(1, 0),(i, 1)]`, i = `sqrt(-1)` and Q = ATBA, then the inverse of the matrix A. Q2021 AT is equal to ______.
Given that A is a square matrix of order 3 and |A| = –2, then |adj(2A)| is equal to ______.
| To raise money for an orphanage, students of three schools A, B and C organised an exhibition in their residential colony, where they sold paper bags, scrap books and pastel sheets made by using recycled paper. Student of school A sold 30 paper bags, 20 scrap books and 10 pastel sheets and raised ₹ 410. Student of school B sold 20 paper bags, 10 scrap books and 20 pastel sheets and raised ₹ 290. Student of school C sold 20 paper bags, 20 scrap books and 20 pastel sheets and raised ₹ 440. |
Answer the following question:
- Translate the problem into a system of equations.
- Solve the system of equation by using matrix method.
- Hence, find the cost of one paper bag, one scrap book and one pastel sheet.
