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A scalar matrix is a diagonal matrix where all the diagonal elements are equal. Therefore, for the given matrix to be a scalar matrix, we must have \(a = d = 5\) and \(b = c = 0\).
Substitute these values into the expression \(a + 2b + 3c + 4d\):
\(a + 2b + 3c + 4d = 5 + 2(0) + 3(0) + 4(5)\)
Simplify the expression:
\(5 + 0 + 0 + 20 = 25\)
Correct Answer: 25