Subtraction of Matrices Exercise (with Solution)

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix Subtraction Question} & \textbf{Answer} \\
\hline
\text{Subtract the following Row Matrices:} \\
A = \begin{pmatrix} 5 & 7 \end{pmatrix}, B = \begin{pmatrix} 3 & 4 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Column Matrices:} \\
A = \begin{pmatrix} 9 \\ 10 \end{pmatrix}, B = \begin{pmatrix} 4 \\ 5 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Square Matrices:} \\
A = \begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix}, B = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Diagonal Matrices:} \\
A = \begin{pmatrix} 5 & 0 \\ 0 & 6 \end{pmatrix}, B = \begin{pmatrix} 3 & 0 \\ 0 & 4 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Scalar Matrices:} \\
A = \begin{pmatrix} 5 & 0 \\ 0 & 5 \end{pmatrix}, B = \begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Identity Matrices:} \\
A = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}, B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Zero Matrices:} \\
A = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}, B = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Symmetric Matrices:} \\
A = \begin{pmatrix} 4 & 3 \\ 3 & 4 \end{pmatrix}, B = \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Skew-Symmetric Matrices:} \\
A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}, B = \begin{pmatrix} 0 & 2 \\ -2 & 0 \end{pmatrix} & ? \\
\hline
\text{Subtract the following Matrix Equality Question:} \\
A = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix}, B = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix} & ? \\
\hline
\end{array}
\]

Solution:

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix Subtraction Question} & \textbf{Answer} \\
\hline
\text{Subtract the following Row Matrices:} \\
A = \begin{pmatrix} 5 & 7 \end{pmatrix}, B = \begin{pmatrix} 3 & 4 \end{pmatrix} & A – B = \begin{pmatrix} 5-3 & 7-4 \end{pmatrix} = \begin{pmatrix} 2 & 3 \end{pmatrix} \\
\hline
\text{Subtract the following Column Matrices:} \\
A = \begin{pmatrix} 9 \\ 10 \end{pmatrix}, B = \begin{pmatrix} 4 \\ 5 \end{pmatrix} & A – B = \begin{pmatrix} 9-4 \\ 10-5 \end{pmatrix} = \begin{pmatrix} 5 \\ 5 \end{pmatrix} \\
\hline
\text{Subtract the following Square Matrices:} \\
A = \begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix}, B = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix} & A – B = \begin{pmatrix} 6-2 & 8-4 \\ 10-6 & 12-8 \end{pmatrix} = \begin{pmatrix} 4 & 4 \\ 4 & 4 \end{pmatrix} \\
\hline
\text{Subtract the following Diagonal Matrices:} \\
A = \begin{pmatrix} 5 & 0 \\ 0 & 6 \end{pmatrix}, B = \begin{pmatrix} 3 & 0 \\ 0 & 4 \end{pmatrix} & A – B = \begin{pmatrix} 5-3 & 0-0 \\ 0-0 & 6-4 \end{pmatrix} = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix} \\
\hline
\text{Subtract the following Scalar Matrices:} \\
A = \begin{pmatrix} 5 & 0 \\ 0 & 5 \end{pmatrix}, B = \begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix} & A – B = \begin{pmatrix} 5-3 & 0-0 \\ 0-0 & 5-3 \end{pmatrix} = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix} \\
\hline
\text{Subtract the following Identity Matrices:} \\
A = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}, B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & A – B = \begin{pmatrix} 2-1 & 0-0 \\ 0-0 & 2-1 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \\
\hline
\text{Subtract the following Zero Matrices:} \\
A = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}, B = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & A – B = \begin{pmatrix} 0-0 & 0-0 \\ 0-0 & 0-0 \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\hline
\text{Subtract the following Symmetric Matrices:} \\
A = \begin{pmatrix} 4 & 3 \\ 3 & 4 \end{pmatrix}, B = \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & A – B = \begin{pmatrix} 4-1 & 3-2 \\ 3-2 & 4-1 \end{pmatrix} = \begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix} \\
\hline
\text{Subtract the following Skew-Symmetric Matrices:} \\
A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}, B = \begin{pmatrix} 0 & 2 \\ -2 & 0 \end{pmatrix} & A – B = \begin{pmatrix} 0-0 & 1-2 \\ -1+2 & 0-0 \end{pmatrix} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \\
\hline
\text{Subtract the following Matrix Equality Question:} \\
A = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix}, B = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix} & A – B = \begin{pmatrix} 3-3 & 5-5 \\ 7-7 & 9-9 \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\hline
\end{array}
\]

Exercise #2

Solution:

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix Subtraction Question} & \textbf{Answer} \\
\hline
\text{Subtract the following 2×3 Matrices:} \\
A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}, B = \begin{pmatrix} 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix} & A – B = \begin{pmatrix} 1-7 & 2-8 & 3-9 \\ 4-10 & 5-11 & 6-12 \end{pmatrix} = \begin{pmatrix} -6 & -6 & -6 \\ -6 & -6 & -6 \end{pmatrix} \\
\hline
\text{Subtract the following 3×2 Matrices:} \\
A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}, B = \begin{pmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{pmatrix} & A – B = \begin{pmatrix} 1-7 & 2-8 \\ 3-9 & 4-10 \\ 5-11 & 6-12 \end{pmatrix} = \begin{pmatrix} -6 & -6 \\ -6 & -6 \\ -6 & -6 \end{pmatrix} \\
\hline
\text{Subtract the following 4×2 Matrices:} \\
A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8 \end{pmatrix}, B = \begin{pmatrix} 9 & 10 \\ 11 & 12 \\ 13 & 14 \\ 15 & 16 \end{pmatrix} & A – B = \begin{pmatrix} 1-9 & 2-10 \\ 3-11 & 4-12 \\ 5-13 & 6-14 \\ 7-15 & 8-16 \end{pmatrix} = \begin{pmatrix} -8 & -8 \\ -8 & -8 \\ -8 & -8 \\ -8 & -8 \end{pmatrix} \\
\hline
\text{Subtract the following 3×4 Matrices:} \\
A = \begin{pmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \end{pmatrix}, B = \begin{pmatrix} 13 & 14 & 15 & 16 \\ 17 & 18 & 19 & 20 \\ 21 & 22 & 23 & 24 \end{pmatrix} & A – B = \begin{pmatrix} 1-13 & 2-14 & 3-15 & 4-16 \\ 5-17 & 6-18 & 7-19 & 8-20 \\ 9-21 & 10-22 & 11-23 & 12-24 \end{pmatrix} = \begin{pmatrix} -12 & -12 & -12 & -12 \\ -12 & -12 & -12 & -12 \\ -12 & -12 & -12 & -12 \end{pmatrix} \\
\hline
\end{array}
\]

Solution:

Exercise #2

Solution:

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