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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES2 Marks
Question
If $\text{P}=\begin{bmatrix}\text{x}&0&0\\0&\text{y}&0\\0&0&\text{z}\end{bmatrix}$ and $\text{Q}=\begin{bmatrix}\text{a}&0&0\\0&\text{b}&0\\0&0&\text{c}\end{bmatrix},$ then prove that $\text{PQ}=\begin{bmatrix}\text{xa}&0&0\\0&\text{yb}&0\\0&0&\text{zc}\end{bmatrix}=\text{QP}.$
✓

Answer

$\text{PQ}=\begin{bmatrix}\text{x}&0&0\\0&\text{y}&0\\0&0&\text{z}\end{bmatrix}\begin{bmatrix}\text{a}&0&0\\0&\text{b}&0\\0&0&\text{c}\end{bmatrix}$$=\begin{bmatrix}\text{xa}&0&0\\0&\text{yb}&0\\0&0&\text{zc}\end{bmatrix}\ ....(\text{i})$
and $\text{QP}=\begin{bmatrix}\text{a}&0&0\\0&\text{b}&0\\0&0&\text{c}\end{bmatrix}\begin{bmatrix}\text{x}&0&0\\0&\text{y}&0\\0&0&\text{z}\end{bmatrix}$
$=\begin{bmatrix}\text{ax}&0&0\\0&\text{by}&0\\0&0&\text{cz}\end{bmatrix}\ ....(\text{ii})$
Thus, we see that, PQ = QP [using Eq. (i) and (ii)]
Hence proved.

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