Solved Examples of multiplication of matrices
In this post, there are are solved examples of matrices. If you found any mistake then comment me.
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Let
A=\left[\begin{array}{ccc}2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4\end{array}\right]and
B =\left[\begin{array}{ccc}-1 & 3 & 5 \\ 1 & -3 & -5 \\ -1 & 3 & 5\end{array}\right]Quesction: Find A+B
A + B=\left[\begin{array}{ccc}2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4\end{array}\right]+\left[\begin{array}{ccc}-1 & 3 & 5 \\ 1 & -3 & -5 \\ -1 & 3 & 5\end{array}\right]A+B=\left[\begin{array}{ccc}
\,\ 2-1 & -3+3 & -5+5 \\
-1+1 & 4-3 & 4-5 \\
\,\ 1-1 & -3+3 & -4+5
\end{array}\right] \\=\left[\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & -1 \\
0 & 0 & 1
\end{array}\right]Question: Find A-B
A - B=\left[\begin{array}{ccc}2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4\end{array}\right]-\left[\begin{array}{ccc}-1 & 3 & 5 \\ 1 & -3 & -5 \\ -1 & 3 & 5\end{array}\right]A-B=\left[\begin{array}{ccc}
\,\ 2+1 & -3-3 & -5-5 \\
-1-1 & \,\ 4+3 & \,\ 4+5 \\
\,\ 1+1 & -3-3 & -4-5
\end{array}\right] \\=\left[\begin{array}{ccc}
3 & -6 & -10 \\
-2 & 7 & 10 \\
2 & -6 & -9
\end{array}\right]Question: Find 2A+3B
2 A+3B=2\left[\begin{array}{ccc}2 & -3 & -5 \\ -1 & 4 & 3 \\ 1 & -3 & -4\end{array}\right]+3\left[\begin{array}{ccc}-1 & 3 & 5 \\ 1 & -3 & -2 \\ -1 & 3 & 5\end{array}\right]=\left[\begin{array}{ccc}
4 & -6 & -10 \\
-2 & 8 & 6 \\
2 & -6 & -8
\end{array}\right]+\left[\begin{array}{ccc}
-3 & 9 & 15 \\
3 & -9 & -6 \\
-3 & 9 & 15
\end{array}\right]=\left[\begin{array}{ccc}
4-3 & -6+9 & -10+15 \\-2+3 & 8-9 & 6-6 \\
2-3 & -6+9 & -8+15
\end{array}\right] \\
=\left[\begin{array}{ccc}
1 & 3 & 5 \\
1 & -1 & 0 \\
-1 & 3 & 7
\end{array}\right]Question: Find AB
AB=\left[\begin{array}{ccc}2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4\end{array}\right]\left[\begin{array}{ccc}-1 & 3 & 5 \\ 1 & -3 & -5 \\ -1 & 3 & 5\end{array}\right]=\left[\begin{array}{ccc}
-2-3+5 & 6+9-15 & 10+15-25 \\1+4 -5& -3-12+15 & -5-20+25\\-1-3+4 & 3+9-12 & 5+15-20
\end{array}\right] \\=\left[\begin{array}{ccc}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{array}\right]