Assertion : If [ ll 1 & 2 3 & 4 ] X= [ l 2 1 ], then the order of… - Vidyadip

MCQ

Assertion : If $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] X=\left[\begin{array}{l}2 \\ 1\end{array}\right]$, then the order of matrix $X$ is $1 \times 2$.
Reason : The product $A B$ of two matrices $A$ and $B$ is possible if number of columns in $A$ is equal to the number of rows in B. Also, the order of the product matrix $A B$ is number of rows in $A X$ number of columns in B.

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
✓
Assertion is incorrect but reason is correct.

✓

Answer

Correct option: D.

Assertion is incorrect but reason is correct.

(d) Assertion is incorrect and reason is correct.
Explanation:
$\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]_{2 \times 2}[ X ]_{p \times q}=\left[\begin{array}{l}2 \\ 1\end{array}\right]_{2 \times 1}$
$\therefore 2=p$
and $2 \times q=2 \times 1$
$\Rightarrow q=1, p=2$
So, the order of matrix $X$ is $2 \times 1$.

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