Question

If Q = [[2, 2], [8, 1]] and R = [[-3, 1], [8, -7]], is the following statement true or false? QR = RQ (true/false)

Answer 1

Upon calculating the matrix products QR and RQ for the given matrices, we find that QR does not equal RQ. Therefore, the statement QR = RQ is false.

Step-by-step explanation:

The student has asked whether the statement QR = RQ is true or false for the given matrices Q = [[2, 2], [8, 1]] and R = [[-3, 1], [8, -7]]. To determine the truth of this statement, we must calculate the matrix products QR and RQ and then compare them.

First, we find the product QR:

• (2*-3 + 2*8) = (2*1 + 2*-7) = [10, -12]
• (8*-3 + 1*8) = (8*1 + 1*-7) = [-16, 1]

So QR = [[10, -12], [-16, 1]].

Next, we calculate the product RQ:

• (-3*2 + 1*8) = (-3*2 + 1*1) = [2, -5]
• (8*2 + -7*8) = (8*2 + -7*1) = [16, 9]

Therefore, RQ = [[2, -5], [16, 9]].

Comparing the two results, we see that QR ≠ RQ. Thus, the statement QR = RQ is false.