Let A = begin{bmatrix} -3 & 2 1 & 4 end{bmat | vedclass

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

Question

(A) Step $1$: Calculate $A^2 = A 	imes A = \begin{bmatrix} -3 & 2 \ 1 & 4 \end{bmatrix} \begin{bmatrix} -3 & 2 \ 1 & 4 \end{bmatrix} = \begin{bmatr

Vedclass · Accepted Answer

$p = -2, q = -1$

Vedclass · Answer

(A) Step $1$: Calculate $A^2 = A 	imes A = \begin{bmatrix} -3 & 2 \ 1 & 4 \end{bmatrix} \begin{bmatrix} -3 & 2 \ 1 & 4 \end{bmatrix} = \begin{bmatrix} (-3)(-3)+(2)(1) & (-3)(2)+(2)(4) \ (1)(-3)+(4)(1) & (1)(2)+(4)(4) \end{bmatrix} = \begin{bmatrix} 11 & 2 \ 1 & 18 \end{bmatrix}$.Step $2$: Calculate $2A = 2 \begin{bmatrix} -3 & 2 \ 1 & 4 \end{bmatrix} = \begin{bmatrix} -6 & 4 \ 2 & 8 \end{bmatrix}$.Step $3$: Calculate $A^2 - 2A + I = \begin{bmatrix} 11 & 2 \ 1 & 18 \end{bmatrix} - \begin{bmatrix} -6 & 4 \ 2 & 8 \end{bmatrix} + \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.Step $4$: Perform the matrix subtraction and addition: $\begin{bmatrix} 11 - (-6) + 1 & 2 - 4 + 0 \ 1 - 2 + 0 & 18 - 8 + 1 \end{bmatrix} = \begin{bmatrix} 18 & -2 \ -1 & 11 \end{bmatrix}$.Step $5$: Comparing with $\begin{bmatrix} 18 & p \ q & 11 \end{bmatrix}$, we get $p = -2$ and $q = -1$.

Let $A = \begin{bmatrix} -3 & 2 \\ 1 & 4 \end{bmatrix}$. If $A^2 - 2A + I = \begin{bmatrix} 18 & p \\ q & 11 \end{bmatrix}$, find the values of $p$ and $q$.

Similar Questions

The number of symmetric matrices of order $3 \times 3$,with all the entries from the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$,is:

Choose the correct statement regarding matrices.

If $A^2 = A$,then $(I + A)^3 - 7A =$ . . . . . . ,where $A$ is a square matrix.

Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A^{2}$ is $1,$ then the possible number of such matrices is

If $A$ and $B$ are two matrices such that $AB$ is an identity matrix and the order of matrix $B$ is $3 \times 4$,then the order of matrix $A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module