MATHEMATICS

JAMB 2002 - Question 16

Mathematics 2002 JAMB Past Questions - Question 16: If p ≤ (2 1)(-3 0)> and I is a 2x2 unit matrix, evaluate p² -2p +41

If p ≤ (2 1)(-3 0)> and I is a 2x2 unit matrix, evaluate p² -2p +41
A:
B:
C:
D:
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Correct Answer

C

Explanation

To evaluate p² - 2p + 41, we need to find the square of matrix p and then perform the necessary matrix operations.Given p = [(2, 1), (-3, 0)] and I is a 2x2 unit matrix, we can proceed as follows:First, let's find p² by multiplying matrix p by itself:p² = p * pp² = [(2, 1), (-3, 0)] * [(2, 1), (-3, 0)]p² = [(2*2 + 1*(-3), 2*1 + 1*0), (-3*2 + 0*(-3), -3*1 + 0*0)]p² = [(4 - 3, 2 + 0), (-6 + 0, -3 + 0)]p² = [(1, 2), (-6, -3)]Next, let's evaluate -2p by multiplying matrix p by -2:-2p = -2 * [(2, 1), (-3, 0)]-2p = [(-2*2, -2*1), (-2*(-3), -2*0)]-2p = [(-4, -2), (6, 0)]Finally, let's add p², -2p, and 41:p² - 2p + 41 = [(1, 2), (-6, -3)] + [(-4, -2), (6, 0)] + [(41, 41), (41, 41)]p² - 2p + 41 = [(1 - 4 + 41, 2 - 2 + 41), (-6 + 6 + 41, -3 + 0 + 41)]p² - 2p + 41 = [(38, 41), (41, 38)]Therefore, the value of p² - 2p + 41 is [(38, 41), (41, 38)].