If \(\begin{bmatrix}2a + b&a - 2b\\5 - c&4\end{bmatrix} = \begin{bmatrix}4&-3\\3&4\end{bmatrix}\), then the value of \(a + b + c\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
Two matrices are equal when they have the same order and their corresponding elements are equal. Comparing the elements:
\(2a + b = 4\)
\(a - 2b = -3\)
\(5 - c = 3\)
Multiplying the first equation by 2 and adding the second:
\(5a = 5\)
\(a = 1\)
Then
\(b = 4 - 2a = 2\)
\(c = 5 - 3 = 2\)
Hence
\(a + b + c = 1 + 2 + 2 = 5\)