Advertisements
Advertisements
Question
|A–1| ≠ |A|–1, where A is non-singular matrix.
Options
True
False
Solution
This statement is False.
Explanation:
Since |A–1| = |A|–1 = for a non-singular matrix.
APPEARS IN
RELATED QUESTIONS
Verify A (adj A) = (adj A) A = |A|I.
`[(2,3),(-4,-6)]`
Find the inverse of the matrices (if it exists).
`[(2,-2),(4,3)]`
Find the inverse of the matrices (if it exists).
`[(-1,5),(-3,2)]`
Find the inverse of the matrices (if it exists).
`[(1,-1,2),(0,2,-3),(3,-2,4)]`
For the matrix A = `[(3,2),(1,1)]` find the numbers a and b such that A2 + aA + bI = O.
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,-2,1),(-2,3,1),(1,1,5)]` verify that
- [adj A]–1 = adj (A–1)
- (A–1)–1 = A
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.
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 \[A^{- 1} A = I_3\]
Given \[A = \begin{bmatrix}2 & - 3 \\ - 4 & 7\end{bmatrix}\], compute A−1 and show that \[2 A^{- 1} = 9I - A .\]
Show that \[A = \begin{bmatrix}5 & 3 \\ - 1 & - 2\end{bmatrix}\] satisfies the equation \[x^2 - 3x - 7 = 0\]. Thus, find A−1.
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 inverse by using elementary row transformations:
\[\begin{bmatrix}3 & 10 \\ 2 & 7\end{bmatrix}\]
If A is symmetric matrix, write whether AT is symmetric or skew-symmetric.
If A is a square matrix, then write the matrix adj (AT) − (adj A)T.
If \[A = \begin{bmatrix}2 & 3 \\ 5 & - 2\end{bmatrix}\] be such that \[A^{- 1} = k A,\] then find the value of k.
If \[A = \begin{bmatrix}2 & 3 \\ 5 & - 2\end{bmatrix}\] , write \[A^{- 1}\] in terms of A.
If A is an invertible matrix of order 3, then which of the following is not true ?
If \[S = \begin{bmatrix}a & b \\ c & d\end{bmatrix}\], then adj A is ____________ .
If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is _____________ .
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 _____________ .
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 _______________ .
If the equation a(y + z) = x, b(z + x) = y, c(x + y) = z have non-trivial solutions then the value of `1/(1+"a") + 1/(1+"b") + 1/(1+"c")` is ____________.
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)
