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# 1.2 Elementary Matrix Operations

Contents

• 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]

### Scalar Multiplication

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