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

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

Question

(C) Let $P = \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix}$ and $Q = \begin{bmatrix} -3 & 2 \ 5 & -3 \end{bmatrix}$. The equation is $PAQ = I$,where $

Vedclass · Accepted Answer

$\begin{bmatrix} 1 & 1 \ 1 & 0 \end{bmatrix}$

Vedclass · Answer

(C) Let $P = \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix}$ and $Q = \begin{bmatrix} -3 & 2 \ 5 & -3 \end{bmatrix}$. The equation is $PAQ = I$,where $I$ is the identity matrix. Then $A = P^{-1} I Q^{-1} = P^{-1} Q^{-1} = (QP)^{-1}$. First,calculate $QP$: $QP = \begin{bmatrix} -3 & 2 \ 5 & -3 \end{bmatrix} \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} = \begin{bmatrix} (-3)(2) + (2)(3) & (-3)(1) + (2)(2) \ (5)(2) + (-3)(3) & (5)(1) + (-3)(2) \end{bmatrix} = \begin{bmatrix} 0 & 1 \ 1 & -1 \end{bmatrix}$. Now,find $A = (QP)^{-1}$. The determinant $|QP| = (0)(-1) - (1)(1) = -1$. $A = \frac{1}{-1} \begin{bmatrix} -1 & -1 \ -1 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 1 \ 1 & 0 \end{bmatrix}$.

If $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$,then $A=$

Similar Questions

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$,then $A^{-1}$ is equal to

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$,$10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]$ and $B$ is the inverse of $A$,then the value of $\alpha$ is

If $A = f(x) = \begin{bmatrix} \cos x & \sin x & 0 \\ -\sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$,then $A^{-1}$ is equal to:

Let $A = \begin{bmatrix} \frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}} \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -i \\ 0 & 1 \end{bmatrix}$,where $i = \sqrt{-1}$. If $M = A^{T}BA$,then the inverse of the matrix $AM^{2023}A^{T}$ is $.........$

If $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}$,then $B^{-1} A^{-1} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module