1. Definition and Examples
1. Addition of matrices
If `A=[[a_11,a_12,a_13],[a_21,a_22,a_23]]` and `B=[[b_11,b_12,b_13],[b_21,b_22,b_23]]` then
`A + B = [[a_11,a_12,a_13],[a_21,a_22,a_23]]+[[b_11,b_12,b_13],[b_21,b_22,b_23]]`
`= [[a_11+b_11,a_12+b_12,a_13+b_13],[a_21+b_21,a_22+b_22,a_23+b_23]]`
2. Substraction of matrices
If `A=[[a_11,a_12,a_13],[a_21,a_22,a_23]]` and `B=[[b_11,b_12,b_13],[b_21,b_22,b_23]]` then
`A - B = [[a_11,a_12,a_13],[a_21,a_22,a_23]]-[[b_11,b_12,b_13],[b_21,b_22,b_23]]`
`= [[a_11-b_11,a_12-b_12,a_13-b_13],[a_21-b_21,a_22-b_22,a_23-b_23]]`
3. Properties of Matrix Addition
1. Matrix Addition is Commutative
`A+B = B+A`
2. Matrix Addition is Associative
`A+(B+C) = (A+B)+C`
3. `A+O=O+A=A`
5. `A+B=O` if and only if `B=-A`
Examples
1. Find `A + B` ...
`A=[[3,1,1],[-1,2,1],[1,1,1]]`,`B=[[5,0,-2],[7,-6,0],[1,1,2]]`
Solution:
| `A + B` | = | | `3` | `1` | `1` | | | `-1` | `2` | `1` | | | `1` | `1` | `1` | |
| + | | `5` | `0` | `-2` | | | `7` | `-6` | `0` | | | `1` | `1` | `2` | |
| = | | `8` | `1` | `-1` | | | `6` | `-4` | `1` | | | `2` | `2` | `3` | |
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2. Find `A - B` ...
`A=[[2,3,1],[0,5,6],[1,1,2]]`,`B=[[2,1,1],[-1,2,1],[1,1,1]]`
Solution:
| `A - B` | = | | `2` | `3` | `1` | | | `0` | `5` | `6` | | | `1` | `1` | `2` | |
| - | | `2` | `1` | `1` | | | `-1` | `2` | `1` | | | `1` | `1` | `1` | |
| = | | `0` | `2` | `0` | | | `1` | `3` | `5` | | | `0` | `0` | `1` | |
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This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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