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MATRIX MATHEMATICS EXAMPLES
Example 1: Addition and Subtraction
Add the following matrices:

|A| = ||||| 1 0 1       0 1 0       1 0 1 |||||
|B| = ||||| 1 5 3       0 14 7       0 0 8 |||||
Answer:
|A| + |B| = ||||| 2 5 4       0 15 7       1 0 9 |||||
Subtract |A| from |B|:
Answer:
|B| − |A| = ||||| 0 5 2       0 13 7        − 1 0 7 |||||
Add the following two matrices:

|C| = ||||| 5 3     14 7     0 8 |||||
|D| = ||||| 1 0 0       1 1 0       1 1 1 |||||
Answer: It’s impossible since the size of |C| is not equal to the size of |D|.
Example 2: Matrix Multiplication
Multiply |A| and |B|:
Answer:
|A| × |B| = ||||| 1*1 + 0*0 + 1*0 1*5 + 0*14 + 1*0 1*2 + 0*7 + 1*8       0*1 + 1*0 + 0*0 0*5 + 1*14 + 0*0 0*3 + 1*7 + 0*8       1*1 + 0*0 + 1*0 1*5 + 0*14 + 1*0 1*2 + 0*7 + 1*8 |||||
|A| × |B| = ||||| 1 5 10       0 14 7       1 5 10 |||||
Example 3: Matrix Transpose
Transpose matrix |B|:
Answer:
|B|T = ||||| 1 0 0       5 14 0       3 7 8 |||||