Question

I don’t know if you could help with both but i’m confused and so is my partner.

Answer 1

Two matrices can be added if and only if they both have the same dimensions. The addition of the matrices is accomplished by adding corresponding elements, therefore, all elements must have corresponding elements in the second matrix to have a defined solution.

The size of the new matrix is the size of the two matrices that combine to form the result. This means that if two M x N matrices are added, the result is an M x N matrix as well.

Consider the addition of two 3 x 3 matrices below:

`\begin{bmatrix}{1} & {2} & {3} \\ {4} & {5} & {6} \\ {7} & {8} & {9}\end{bmatrix}+\begin{bmatrix}{1} & {4} & {7} \\ {2} & {5} & {8} \\ {3} & {6} & {9}\end{bmatrix}=\begin{bmatrix}{1}+1 & 2+4 & {3+7} \\ {4+2} & {5+5} & {6+8} \\ {7+3} & {8+6} & {9+9}\end{bmatrix}=\begin{bmatrix}{2} & {6} & {10} \\ {6} & {10} & {14} \\ {10} & {14} & {18}\end{bmatrix}`

The resultant matrix can be seen to be a 3 x 3 matrix as well.

Therefore, if we are to add Matrix D and Matrix E, both 6 x 7 matrices, the new matrix will be a 6 x 7 matrix as well.