MULTIPLYING 2 CROSS 2 MATRIX
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The product of an m x n matrix A with an n x p matrix B, is the m x p matrix AB in which the element in the rth row and cth column is the sum of the product of the elements in the rth row of A with the corresponding elements in the cth column of B.
Note :
The product of AB exists only if the number of rows of A equals the number of columns of B.
Problem 1 :
- 5 1 1 5 · 3 - 5 6 - 4
Solution :
- 5 1 1 5 · 3 - 5 6 - 4 = - 5 1 × 3 6 - 5 1 × - 5 - 4 1 5 × 3 6 1 5 × - 5 - 4 = ( - 15 + 6 ) ( 25 - 4 ) ( 3 + 30 ) ( - 5 - 20 ) = - 9 21 33 - 25
Problem 2 :
- 3 4 · - 3 - 6 3 - 6
Solution :
- 3 4 · - 3 - 6 3 - 6 = - 3 4 × - 3 3 - 3 4 × - 6 - 6 = ( 9 + 12 ) ( 18 - 24 ) = 21 - 6
Problem 3 :
2 - 1 - 5 - 6 · 6 0 - 1 0
Solution :
2 - 1 - 5 - 6 · 6 0 - 1 0 = 2 - 1 × 6 - 1 2 - 1 × 0 0 - 5 - 6 × 6 - 1 - 5 - 6 × 0 0 = ( 12 + 1 ) ( 0 - 0 ) ( - 30 + 6 ) ( 0 - 0 ) = 13 0 - 24 0
Problem 4 :
3 - 6 5 1 · 1 3
Solution :
3 - 6 5 1 · 1 3 = 3 - 6 × 1 3 5 1 × 1 3 = 3 - 18 5 + 3 = - 15 8
Problem 5 :
- 3 2 · 6 - 6
Solution :
- 3 2 · 6 - 6 = - 3 × 6 - 3 ×- 6 2 × 6 2 × - 6 = - 18 18 12 - 12
Problem 6 :
- 3 0 - 2 - 4 - 3 1 · 3 6 - 4 2
Solution :
- 3 0 - 2 - 4 - 3 1 · 3 6 - 4 2 = - 3 0 × 3 - 4 - 3 0 × 6 2 - 2 - 4 × 3 - 4 - 2 - 4 × 6 2 - 3 1 × 3 - 4 - 3 1 × 6 2 = ( - 9 - 0 ) ( - 18 + 0 ) ( - 6 + 16 ) ( - 12 - 8 ) ( - 27 - 4 ) ( - 18 + 2 ) = - 9 - 18 10 - 20 - 31 - 16
Problem 7 :
5 - 2 · - 2 - 4 - 3 - 3
Solution :
5 - 2 · - 2 - 4 - 3 - 3 = 5 - 2 × - 2 - 3 5 - 2 × - 4 - 3 = ( - 10 + 6 ) ( - 20 + 6 ) = - 4 - 14
Problem 8 :
- 2 1 6 - 1 · 1 - 4 5 - 3
Solution :
- 2 1 6 - 1 · 1 - 4 5 - 3 = - 2 1 × 1 5 - 2 1 × - 4 - 3 6 - 1 × 1 5 6 - 1 × - 4 - 3 = ( - 2 + 5 ) ( 8 - 3 ) ( 6 - 5 ) ( - 24 + 3 ) = 3 5 1 - 21
Problem 9 :
- 6 - 5 - 5 4 · 0 3
Solution :
- 6 - 5 - 5 4 · 0 3 = - 6 - 5 × 0 3 - 5 4 × 0 3 = 0 - 15 0 + 12 = - 15 12
Problem 10 :
- 4 2 2 5 · - 3 0 - 3 5
Solution :
- 4 2 2 5 · - 3 0 - 3 5 = - 4 2 × - 3 - 3 - 4 2 × 0 5 2 5 × - 3 - 3 2 5 × 0 5 = ( 12 - 6 ) ( 0 + 10 ) ( - 6 - 15 ) ( 0 + 25 ) = 6 10 - 21 25
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