Find the determinant of the matrix \(\begin{pmatrix} 2 & 0 & 1 \\ 3 & 2 & 4 \\ 1 & 4 & 1 \end{pmatrix}\)
A
-16
B
16
C
-18
D
18
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\begin{pmatrix} 2 & 0 & 1 \\ 3 & 2 & 4 \\ 1 & 4 & 1 \end{pmatrix}\) = 2\(\begin{pmatrix} 2& 4 \\ 4 & 1 \end{pmatrix}\) - 0\(\begin{pmatrix} 3 & 4 \\ 1 & 1 \end{pmatrix}\) + 1\(\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix}\)
= 2(2 - 16) - 0 + 1(12 - 2)
= 2(-14) + 1(10)
= - 28 + 10 = - 18.
Source: Myschool Past Questions Archive (Record #78184)