If \(f(x)=3x-2\), \(P=\begin{pmatrix}2 & 1 \\ -1 & 0\end{pmatrix}\) and I is 2 X 2 identity matrix, evaluate \(f(P)\)

Answer Details

To evaluate f(P), we need to substitute P into the function f(x) = 3x - 2. However, P is a matrix, not a scalar value, so we need to apply the function to each element of the matrix separately. So, we have: f(P) = ( 3(2) - 2 3(1) - 2 3(-1) - 2 3(0) - 2 3(3) - 2 3(2) - 2 ) = ( 4 1 -5 -2 7 4 ) Therefore, the answer is the matrix with the entries: ( 4 1 -5 -2 7 4 ) which corresponds to option (D) (43-3-2).