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 the off-diagonal elements are zero and all the diagonal elements are equal. The third diagonal element is 5, so
\(b = 0,\quad c = 0\)
\(a = 5,\quad d = 5\)
Hence
\(a + 2b + 3c + 4d = 5 + 0 + 0 + 20\)
\(= 25\)