## 1.2 Elementary Matrix Operations

### Addition and Subtraction

**Matrix addition and subtraction**is carried out on an**element-by-element**basis. The element C_{i,j} in the resultant matrix is found by carrying out addition or subtraction with the corresponding elements; A_{i,j} and B_{i,j} in the other matrices.- Matrices can
**only**be added or subtracted from one another if they have the**same dimensions**.

Examples

\left[\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right]+\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right]=\left[\begin{array}{ll} 2 & 2 \\ 1 & 1 \end{array}\right]

\left[\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right]-\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right]=\left[\begin{array}{cc} 0 & 2 \\ -1 & 1 \end{array}\right]