If $\begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix}$ is a scalar matrix, then the value of $a + 2b + 3c + 4d$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $25$ ##
In a scalar matrix, all diagonal elements are equal.
So, $a = d = 5$
$c = b = 0$.
So, the value of $a + 2b + 3c + 4d$
$= 5 + 2(0) + 3(0) + 4(5)$
$= 5 + 20 = 25$.