If A = \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}\). Find AB
A
\(\begin{pmatrix} 18 & 6 \\ 12 & 10 \\ 10 & 6 \end{pmatrix}\)
B
\(\begin{pmatrix} 10 & 6 \\ 13 & 10 \\ 12 & 6 \end{pmatrix}\)
C
\(\begin{pmatrix} 10 & 6 \\ 12 & 10 \\ 11 & 6 \end{pmatrix}\)
D
\(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Given A = \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}\).
We can multiply these matrices since the number of colums in A = number of rows in B
AB = \(\begin{pmatrix} (2*3)+(1*4) & (2*2)+(1*2) \\ (2*3)+(3*4) & (2*2)+(3*2) \\ (1*3)+(2*4) & (1*2)+(2*2) \end{pmatrix}\)
AB = \(\begin{pmatrix} (6+4) & (4+2) \\ (6+12) & (4+6) \\ (3+8) & (2+4) \end{pmatrix}\)
= \(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)
Source: Myschool Past Questions Archive (Record #64273)