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In the Following Matrix Equation Use Elementary Operation R2 → R2 + R1 and the Equation Thus Obtained: [ 2 3 1 4 ] [ 1 0 2 − 1 ] = [ 8 − 3 9 − 4 ] - Mathematics

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Question

In the following matrix equation use elementary operation R2 → R2 + Rand the equation thus obtained:

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]

Solution

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]

By applying elementary operation R2 → R2 + R1, we get

\[\begin{bmatrix}2 & 3 \\ 3 & 7\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 17 & - 7\end{bmatrix}\]
(Every row operation is equivalent to left-multiplication by an elementary matrix.)
 
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Chapter 7: Adjoint and Inverse of a Matrix - Exercise 7.3 [Page 36]

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RD Sharma Mathematics [English] Class 12
Chapter 7 Adjoint and Inverse of a Matrix
Exercise 7.3 | Q 30 | Page 36

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