A matrix can only be added to another matrix if the two matrices have the same dimensions .
To add two matrices, just add the corresponding entries, and place this sum in the corresponding position in the matrix which results.
Adding 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 sum simply by adding the corresponding entries in matrices A and B. This is shown below.
A+B=\[\begin{bmatrix} 4& 8 \\ 3 & 7 \\ \end{bmatrix}\]+\[\begin{bmatrix} 1& 0 \\ 5& 2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 4+1& 8+0 \\ 3+7&7+2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 5&8 \\ 8& 9 \\ \end{bmatrix}\]
Adding 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 sum simply by adding the corresponding entries in matrices A and B. This is shown below.
A+B=\[\begin{bmatrix} 3 &4 & 5 \\ 4 &8 & 9 \\ 2& 1 &5 \\ \end{bmatrix}\]+\[\begin{bmatrix} 7 &8 & 5 \\ 7 &5 & 6 \\ 4& 3 &2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 3+7& 4+8 & 5+5 \\ 4+7&8+5 & 9+6 \\ 2+4 & 1+3& 5+2 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 10 & 12 & 10 \\ 11& 13 &15 \\ 6 & 4 & 7\\ \end{bmatrix}\]
Adding 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 sum simply by adding the corresponding entries in matrices A and B. This is shown below.
A+B=\[\begin{bmatrix} 2&3 &3 & 4 \\ 4 & 8 &0 & 1 \\ 9&2 &3 &2 \\ 5 &7 & 3 &1 \\ \end{bmatrix}\]+\[\begin{bmatrix} 4& 6 &2 &0 \\ 3 & 6 & 4 &2 \\ 5 & 7 &5 &1 \\ 9 & 2 & 1 &3 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 2+4&3+6 &3+2 &4+0 \\ 4+3 &8+6 &0+4 &1+2 \\ 9+5 &2+7 &3+5 &2+1 \\ 5+9 & 7+2 &3+1 & 1+3 \\ \end{bmatrix}\]
=\[\begin{bmatrix} 6& 9 & 5 & 4 \\ 7& 14&4 & 3\\ 14&9 & 8 &3 \\ 14&9 & 4 &4 \\ \end{bmatrix}\]
