If A = begin{bmatrix} 3 & 1 -1 & 2 end{bmatr | vedclass

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

Question

(D) Given that,$A = \begin{bmatrix} 3 & 1 \ -1 & 2 \end{bmatrix}$.First,we calculate $A^{2} = A 	imes A$:$A^{2} = \begin{bmatrix} 3 & 1 \ -1 & 2 \e

Vedclass · Accepted Answer

$-7I$

Vedclass · Answer

(D) Given that,$A = \begin{bmatrix} 3 & 1 \ -1 & 2 \end{bmatrix}$.First,we calculate $A^{2} = A 	imes A$:$A^{2} = \begin{bmatrix} 3 & 1 \ -1 & 2 \end{bmatrix} \begin{bmatrix} 3 & 1 \ -1 & 2 \end{bmatrix} = \begin{bmatrix} (3)(3) + (1)(-1) & (3)(1) + (1)(2) \ (-1)(3) + (2)(-1) & (-1)(1) + (2)(2) \end{bmatrix} = \begin{bmatrix} 9-1 & 3+2 \ -3-2 & -1+4 \end{bmatrix} = \begin{bmatrix} 8 & 5 \ -5 & 3 \end{bmatrix}$.Next,we calculate $5A$:$5A = 5 \begin{bmatrix} 3 & 1 \ -1 & 2 \end{bmatrix} = \begin{bmatrix} 15 & 5 \ -5 & 10 \end{bmatrix}$.Finally,we compute $A^{2} - 5A$:$A^{2} - 5A = \begin{bmatrix} 8 & 5 \ -5 & 3 \end{bmatrix} - \begin{bmatrix} 15 & 5 \ -5 & 10 \end{bmatrix} = \begin{bmatrix} 8-15 & 5-5 \ -5-(-5) & 3-10 \end{bmatrix} = \begin{bmatrix} -7 & 0 \ 0 & -7 \end{bmatrix}$.This can be written as $-7 \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = -7I$.

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$,then $A^{2} - 5A$ is equal to:

Similar Questions

The number of all $3 \times 3$ matrices $A$,with entries from the set $\{-1, 0, 1\}$ such that the sum of the diagonal elements of $AA^{T}$ is $3$,is

What must be the matrix $X$ if $2X + \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}$?

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$,show that $A^{2} - 5A + 7I = 0$.

If $2\begin{bmatrix} 5 & x \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 1 \\ 1 & y \end{bmatrix} = \begin{bmatrix} 10 & 5 \\ 7 & 0 \end{bmatrix}$,then find the values of $x$ and $y$.

The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module