A matrix can only be subtracted to another matrix if the two matrices have the same dimensions .
To subtracted two matrices, just subtracted the corresponding entries, and place this subtracted numbers in the corresponding position in the matrix which results.
Subtraction of 2x2 matrices:
Given A=\[\begin{bmatrix} 4& 8 \\ 3 & 7 \\ \end{bmatrix}\] and B=\[\begin{bmatrix} 1& 0 \\ 5& 2 \\ \end{bmatrix}\],lets find A-B.
We can find the subtraction simply by subtracting the corresponding entries in matrices A and B. This is shown below.
A-B=\[\begin{bmatrix} 4& 8 \\ 3 & 7 \\ \end{bmatrix}\]-\[\begin{bmatrix} 1& 0 \\ 5& 2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 4-1& 8-0 \\ 3-7&7-2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 3&8 \\ -4& 5 \\ \end{bmatrix}\]
Subtraction of 3x3 matrices:
Given A=\[\begin{bmatrix} 3 &4 & 5 \\ 4 &8 & 9 \\ 2& 1 &5 \\ \end{bmatrix}\]and B= \[\begin{bmatrix} 7 &8 & 5 \\ 7 &5 & 6 \\ 4& 3 &2 \\ \end{bmatrix}\],lets find A-B.
We can find the subtraction simply by subtracting the corresponding entries in matrices A and B. This is shown below.
A-B=\[\begin{bmatrix} 3 &4 & 5 \\ 4 &8 & 9 \\ 2& 1 &5 \\ \end{bmatrix}\]-\[\begin{bmatrix} 7 &8 & 5 \\ 7 &5 & 6 \\ 4& 3 &2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 3-7& 4-8 & 5-5 \\ 4-7&8-5 & 9-6 \\ 2-4 & 1-3& 5-2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} -4 & -4 & 0 \\ -3& 3 &3 \\ 3 & -2 & 3\\ \end{bmatrix}\]
Subtraction of 4x4 matrices:
Given A=\[\begin{bmatrix} 2&3 &3 & 4 \\ 4 & 8 &0 & 1 \\ 9&2 &3 &2 \\ 5 &7 & 3 &1 \\ \end{bmatrix}\] and B=\[\begin{bmatrix} 4& 6 &2 &0 \\ 3 & 6 & 4 &2 \\ 5 & 7 &5 &1 \\ 9 & 2 & 1 &3 \\ \end{bmatrix}\] lets find A-B
We can find the subtraction simply by subtracting the corresponding entries in matrices A and B. This is shown below.
A-B=\[\begin{bmatrix} 2&3 &3 & 4 \\ 4 & 8 &0 & 1 \\ 9&2 &3 &2 \\ 5 &7 & 3 &1 \\ \end{bmatrix}\]-\[\begin{bmatrix} 4& 6 &2 &0 \\ 3 & 6 & 4 &2 \\ 5 & 7 &5 &1 \\ 9 & 2 & 1 &3 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 2-4&3-6 &3-2 &4-0 \\ 4-3 &8-6 &0-4 &1-2 \\ 9-5 &2-7 &3-5 &2-1 \\ 5-9 & 7-2 &3-1 & 1-3 \\ \end{bmatrix}\]
=\[\begin{bmatrix} -2& -3 & 1 & 4 \\ 1& 2&-4 & -1\\ 4&-5 & -2 &1 \\ -4&5 & 2 &-2 \\ \end{bmatrix}\]
