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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\begin{bmatrix}2&1&3 \end{bmatrix}$ $\begin{pmatrix}-1&0&-1\\-1&1&0\\0&1&1 \end{pmatrix}\begin{pmatrix}1\\0\\-1 \end{pmatrix}=\text{A},$ then write the order of matrix A.
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Answer

Consider, $\begin{pmatrix}2&1&3 \end{pmatrix}\begin{pmatrix}-1&0&-1\\-1&1&0\\0&1&1 \end{pmatrix}\begin{pmatrix}1\\0\\-1 \end{pmatrix}=\text{A}$
Order of matrix $\begin{pmatrix}2&1&3 \end{pmatrix}$ is 1 × 3.
Order of matrix $\begin{pmatrix}-1&0&-1\\-1&1&0\\0&1&1 \end{pmatrix}$ is 3 × 3
Order of matrix $\begin{pmatrix}1\\0\\-1 \end{pmatrix}$ is 3 × 1
Therefore, order of $\begin{pmatrix}2&1&3 \end{pmatrix}\begin{pmatrix}-1&0&-1\\-1&1&0\\0&1&1 \end{pmatrix}\begin{pmatrix}1\\0\\-1 \end{pmatrix}$ is 1 × 1.

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