If the matrix A=begin{bmatrix} 1 & 2 & 2 2 & | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the matrix equation $A^2-4A-5I=0$.Multiply both sides by $A^{-1}$:$A^2 A^{-1} - 4A A^{-1} - 5I A^{-1} = 0 A^{-1}$$A - 4I - 5A^{-1} = 0$$5A^{

Vedclass · Accepted Answer

$\frac{1}{5}\begin{bmatrix} -3 & 2 & 2 \ 2 & -3 & 2 \ 2 & 2 & -3 \end{bmatrix}$

Vedclass · Answer

(B) Given the matrix equation $A^2-4A-5I=0$.Multiply both sides by $A^{-1}$:$A^2 A^{-1} - 4A A^{-1} - 5I A^{-1} = 0 A^{-1}$$A - 4I - 5A^{-1} = 0$$5A^{-1} = A - 4I$$A^{-1} = \frac{1}{5}(A - 4I)$Now, substitute the matrix $A$ and $I$:$A^{-1} = \frac{1}{5} \left( \begin{bmatrix} 1 & 2 & 2 \ 2 & 1 & 2 \ 2 & 2 & 1 \end{bmatrix} - 4 \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} ight)$$A^{-1} = \frac{1}{5} \left( \begin{bmatrix} 1 & 2 & 2 \ 2 & 1 & 2 \ 2 & 2 & 1 \end{bmatrix} - \begin{bmatrix} 4 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 4 \end{bmatrix} ight)$$A^{-1} = \frac{1}{5} \begin{bmatrix} 1-4 & 2-0 & 2-0 \ 2-0 & 1-4 & 2-0 \ 2-0 & 2-0 & 1-4 \end{bmatrix}$$A^{-1} = \frac{1}{5} \begin{bmatrix} -3 & 2 & 2 \ 2 & -3 & 2 \ 2 & 2 & -3 \end{bmatrix}$

If the matrix $A=\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$ satisfies the matrix equation $A^2-4A-5I=0$, then $A^{-1}=$

Similar Questions

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{bmatrix}$, then $|\operatorname{Adj}(A^2)| = $

The inverse of the matrix $A = \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}$ is:

Which of the following statements is incorrect for a square matrix $A$ where $|A| \neq 0$?

If possible,using elementary row transformations,find the inverse of the following matrix:
$\left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$

By using elementary operations,find the inverse of the matrix $A=\left[\begin{array}{rr}1 & 2 \\ 2 & -1\end{array}\right]$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module