The order of x& y& z x & h& g & b& f &amp… - Vidyadip

MCQ

The order of $\begin{bmatrix}\text{x}&\text{amp;}\text{ y}&\text{amp; }\text{z}\end{bmatrix}$ $\begin{bmatrix}\text{x} &\text{amp;}\text{ h}&\text{amp;}\text{ g} \\\text{h} &\text{amp;}\text{ b}&\text{amp; }\text{f}\\\text{g} &\text{amp;}\text{ f}&\text{amp; }\text{c} \end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}$ is :

A
$3\times1$
✓
$1\times1$
C
$1\times3$
D
$3\times3$

✓

Answer

Correct option: B.

$1\times1$

Let $\text{ABC}=\begin{bmatrix}\text{x}&\text{amp;}\text{ y}&\text{amp; }\text{z}\end{bmatrix}\begin{bmatrix}\text{x} &\text{amp;}\text{ h}&\text{amp;}\text{ g} \\\text{h} &\text{amp;}\text{ b}&\text{amp; }\text{f}\\\text{g} &\text{amp;}\text{ f}&\text{amp; }\text{c} \end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}$
Here, the order of $\text{A}$ is $1\times3$
Order of $\text{B}$ is $3\times3$
Since, matrix multiplication satisfies associative property
$\text{i}.\text{e}. (\text{AB})\text{C} = \text{A}(\text{BC})$
Hence, the order of $\text{AB}$ is $1\times3$
Hence, the order of $\text{ABC}$ is $1\times1$

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