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If ⎡ ⎢ ⎣ 1 0 0 0 0 1 0 1 0 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ X Y Z ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ 2 − 1 3 ⎤ ⎥ ⎦ , Find X, Y, Z. - Mathematics

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Question

If \[\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix} = \begin{bmatrix}2 \\ - 1 \\ 3\end{bmatrix}\], find x, y, z.

Solution

Here,
\[\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix} = \begin{bmatrix}2 \\ - 1 \\ 3\end{bmatrix} \]
\[ \Rightarrow \begin{bmatrix}x \\ z \\ y\end{bmatrix} = \begin{bmatrix}2 \\ - 1 \\ 3\end{bmatrix}\]
\[ \therefore x = 2, y = 3\text{ and }z = - 1\]

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Chapter 8: Solution of Simultaneous Linear Equations - Exercise 8.3 [Page 21]

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RD Sharma Mathematics [English] Class 12
Chapter 8 Solution of Simultaneous Linear Equations
Exercise 8.3 | Q 5 | Page 21

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