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Question: Which of the following is equivalent to the product matrix (A - B) C? Evaluate it using A = (- 1210), B = (0121) and C = (1111).


A ) AC - BC, (00- 2- 2)
B ) AC, (0- 20- 2)
C ) I, (1001)
D ) BC, (- 20- 20)

Steps to derive

1 A - B = (- 1210) - (0121) = (- 1 - 02 - 11 - 20 - 1) = (-11- 1- 1)

2 (A - B) C = (- 11- 1- 1) (1111) = ((- 1)1 + 1(1)- 1(1) + 1(1)(- 1)1 + (- 1)1- 1(1) + (- 1)1)

3 (A - B) C = (00- 2- 2)

4 AC = (- 1210) (1111) = ((- 1)1 + 2(1)- 1(1) + 2(1)1(1) + 0(1)1(1) + 0(1)) = (1111)

5 BC = (0121) (1111) = (0(1) + 1(1)0(1) + 1(1)2(1) + 1(1)2(1) + 1(1)) = (1133)

6 AC - BC = (1111) - (1133) = (1 - 11 - 11 - 31 - 3) = (00- 2- 2)

7 So, (A - B) C = AC - BC



Hence the right answer is Option A

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