Using elementary transformations,find the inv | vedclass

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

Question

(A) Let $A = \begin{bmatrix} 1 & 2 & 1 \ 3 & 2 & 3 \ 1 & 1 & 2 \end{bmatrix}$. We write $A = IA$: $\begin{bmatrix} 1 & 2 & 1 \ 3 & 2 & 3 \ 1 & 1 &

Vedclass · Accepted Answer

$\begin{bmatrix} -1/4 & 3/4 & -1 \ 3/4 & -1/4 & 0 \ -1/4 & -1/4 & 1 \end{bmatrix}$

Vedclass · Answer

(A) Let $A = \begin{bmatrix} 1 & 2 & 1 \ 3 & 2 & 3 \ 1 & 1 & 2 \end{bmatrix}$. We write $A = IA$: $\begin{bmatrix} 1 & 2 & 1 \ 3 & 2 & 3 \ 1 & 1 & 2 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} A$ Applying $R_2 	o R_2 - 3R_1$ and $R_3 	o R_3 - R_1$: $\begin{bmatrix} 1 & 2 & 1 \ 0 & -4 & 0 \ 0 & -1 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \ -3 & 1 & 0 \ -1 & 0 & 1 \end{bmatrix} A$ Applying $R_2 	o R_2 / (-4)$: $\begin{bmatrix} 1 & 2 & 1 \ 0 & 1 & 0 \ 0 & -1 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \ 3/4 & -1/4 & 0 \ -1 & 0 & 1 \end{bmatrix} A$ Applying $R_1 	o R_1 - 2R_2$ and $R_3 	o R_3 + R_2$: $\begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} -1/2 & 1/2 & 0 \ 3/4 & -1/4 & 0 \ -1/4 & -1/4 & 1 \end{bmatrix} A$ Applying $R_1 	o R_1 - R_3$: $\begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} -1/4 & 3/4 & -1 \ 3/4 & -1/4 & 0 \ -1/4 & -1/4 & 1 \end{bmatrix} A$ Thus,$A^{-1} = \begin{bmatrix} -1/4 & 3/4 & -1 \ 3/4 & -1/4 & 0 \ -1/4 & -1/4 & 1 \end{bmatrix}$.

Using elementary transformations,find the inverse of the following matrix,if it exists: $\begin{bmatrix} 1 & 2 & 1 \\ 3 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix}$

Similar Questions

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $X$ is a $2 \times 2$ matrix such that $AX = I$,then $X =$

Let $A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}$. Verify that $(AB)^{-1} = B^{-1} A^{-1}$.

If $P$ is a $3 \times 3$ real matrix such that $P^{T} = aP + (a - 1)I$,where $a > 1$,then $..........$

The adjoint of the matrix $N = \begin{bmatrix} -4 & -3 & -3 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \end{bmatrix}$ is

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module