MULTIPLYING 2 CROSS 2 MATRIX

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 :

-5 115 · 3-56-4

Solution :

-5 115 · 3-56-4 = -51 × 36-51 × -5-415 × 3615 × -5-4 = (-15 + 6)(25 -4)(3 + 30)(-5 - 20)= -92133-25

Problem 2 :

-34 · -3-63-6

Solution :

-34 · -3-63-6 = -34 × -33-34 × -6-6= (9 + 12)(18 - 24)= 21-6

Problem 3 :

2 -1-5-6 · 60-10

Solution :

2 -1-5-6 · 60-10 = 2-1 × 6-12-1 × 00-5-6 × 6-1-5-6 × 00 = (12 + 1)(0 - 0)(-30 + 6)(0 - 0)= 130-240

Problem 4 :

3-651 ·13

Solution :

3-651 ·13 = 3-6 × 1351 × 13= 3- 185+ 3= -158

Problem 5 :

-32 ·6-6

Solution :

-32 ·6-6= -3 × 6-3 ×-62 × 62 × -6= -181812-12

Problem 6 :

-3 0-2-4-31 · 36-42

Solution :

-3 0-2-4-31 · 36-42 = -30 × 3-4-30 × 62-2-4 × 3-4-2-4 × 62-31 × 3-4-31 × 62 = (-9 - 0)(-18 + 0)(-6 + 16)(-12 - 8)(-27 - 4)(-18 + 2)= -9-1810-20-31-16

Problem 7 :

5-2 · -2-4-3-3

Solution :

5-2 · -2-4-3-3 = 5-2 × -2-35-2 × -4-3= (-10 + 6)(-20 + 6)= -4-14

Problem 8 :

-2 16-1 · 1-45-3

Solution :

-2 16-1 · 1-45-3 = -21 × 15-21 × -4-36-1 × 156-1 × -4-3 = (-2 + 5)(8 - 3)(6 - 5)(-24 + 3)= 351-21

Problem 9 :

-6-5-54 ·03

Solution :

-6-5-54 ·03 = -6-5 × 03-54 × 03= 0- 150+ 12= -1512

Problem 10 :

-4 225 · -30-35

Solution :

-4 225 · -30-35 = -42 × -3-3-42 × 0525 × -3-325 × 05 = (12 - 6)(0 + 10)(-6 - 15)(0 + 25)= 610-2125

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