Let A = \(\begin{pmatrix}2 & -4 & 3\\5 & 1 & 0\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4 & -2\\-3 & 3 & -1\end{pmatrix}\). Find A + 2B
A
\(\begin{pmatrix}4 & 4 & -1\\-1 & 7 & -2\end{pmatrix}\)
B
\(\begin{pmatrix}-1 & 4 & -1\\4 & 7 & -2\end{pmatrix}\)
C
\(\begin{pmatrix}4 & 4 & -1\\7 & 7 & -2\end{pmatrix}\)
D
\(\begin{pmatrix}-1 & 7 & -2\\4 & 4 & -2\end{pmatrix}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
A = \(\begin{pmatrix}2 & -4 & 3\\5 & 1 & 0\end{pmatrix}\), B = \(\begin{pmatrix}1 & 4 & -2\\-3 & 3 & -1\end{pmatrix}\)
2B = 2 x \(\begin{pmatrix}1 & 4 & -2\\-3 & 3 & -1\end{pmatrix}\) = \(\begin{pmatrix}2 & 8 & -4\\-6 & 6 & -2\end{pmatrix}\)
A + 2B = \(\begin{pmatrix}2 & -4 & 3\\5 & 1 & 0\end{pmatrix}\) + \(\begin{pmatrix}2 & 8 & -4\\-6 & 6 & -2\end{pmatrix}\) = \(\begin{pmatrix}4 & 4 & -1\\-1 & 7 & -2\end{pmatrix}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70189)