If f(x) = 3x - 2I, P = \(\begin{pmatrix}2 & 1 \\-1 & 0 \end{pmatrix}\) and I is 2 x 2 identity matrix. Evaluate f(p)
A
\(\begin{pmatrix}6 & -3 \\3 & 0 \end{pmatrix}\)
B
\(\begin{pmatrix}2 & 0 \\0 & 2 \end{pmatrix}\)
C
\(\begin{pmatrix}8 & 3 \\-3 & 2 \end{pmatrix}\)
D
\(\begin{pmatrix}4 & 3 \\-3 & -2 \end{pmatrix}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
I = \(\begin{pmatrix}1 & 0 \\0 & 1 \end{pmatrix}\)
Then, 3x - 2I becomes 3p - 2I (since we are finding f(p))
3\(\begin{pmatrix}2 & 1 \\-1 & 0 \end{pmatrix}\) - 2\(\begin{pmatrix}1 & 0 \\ 0 & 1 \end{pmatrix}\)
= \(\begin{pmatrix}6 & 3 \\-3 & 0 \end{pmatrix}\) - \(\begin{pmatrix}2 & 0 \\ 0 & 2 \end{pmatrix}\)
= \(\begin{pmatrix}4 & 3 \\-3 & -2 \end{pmatrix}\)
Source: Myschool Past Questions Archive (Record #72044)