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:

$25$

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 $a + 2b + 3c + 4d$

$= 5 + 2(0) + 3(0) + 4(5)$

$= 5 + 20 = 25$.