The matrix $A$ satisfying the equation $\begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix} A = \begin{bmatrix} 1 & 1 \\ 0 & -1 \end{bmatrix}$ is (1) $\begin{bmatrix} 1 & 4 \\ -1 & 0 \end{bmatrix}$ (2) $\begin{bmatrix} 1 & -4 \\ 1 & 0 \end{bmatrix}$ (3) $\begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}$ (4) $\begin{bmatrix} 1 & -4 \\ 1 & 1 \end{bmatrix}$

The matrix A satisfying the equation 1 3 \0 1 A = 1 1 \0 -1 is (1) 1 4 \-1 0 (2) 1 -4 \1 0 (3) 1 4 \0 -1 (4) 1

Exercise 7.5 · Q23

A

(1)

\begin{bmatrix} 1 & 4 \\ -1 & 0 \end{bmatrix}

(2)

\begin{bmatrix} 1 & -4 \\ 1 & 0 \end{bmatrix}

(3)

\begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}

(4)

\begin{bmatrix} 1 & -4 \\ 1 & 1 \end{bmatrix}

Tamil Nadu DgeTextbookSubjectiveImportance★★★★★

73% · 80/110 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Solve $PA = Q$ by $A = P^{-1}Q$ .

This tests solving a matrix equation.

Step 1. Let $P = \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}$ . Since $\det P = 1$ , $P^{-1} = \begin{bmatrix} 1 & -3 \\ 0 & 1 \end{bmatrix}$ .

Step 2. Then $A = P^{-1}Q = \begin{bmatrix} 1 & -3 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} 1 & 1 \\ 0 & -1 \end{bmatrix}$ . …