If A = -1 & 0 & 0 0 & x & 0 0 & 0 & m is … - Vidyadip

MCQ

If $\text{A} =\displaystyle \begin{bmatrix} -1 &\text{amp; } 0 &\text{amp; }0 \\ 0 &\text{amp; }\text{x} &\text{amp; } 0 \\ 0 &\text{amp; } 0 &\text{amp; }\text{m} \end{bmatrix}$is a scalar matrix then $\text{x}+\text{m}=$

A
$0$
B
$-1$
✓
$-2$
D
$-3$

✓

Answer

Correct option: C.

$-2$

A scalar matrix has all the elements of the diagonals same.
For example : $ \begin{bmatrix} 3 &\text{amp; } 0\\ 0&\text{amp; } 3 \end{bmatrix}$
In our case $A$ is given to be a scalar matrix hence all the diagonal elements must be same.
So, $\text{x} = \text{m} = -1$
And $\text{x}+\text{m} = -1 -1 = -2$

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