Two matrices P and Q are defined as:
P = [[3, k], [2, 5]] and Q = [[1, -2], [0, 4]]
where k is a real constant.

(a) Find PQ in terms of k. [3 marks]
(b) Given that det(PQ) = 46, find the value of k. [4 marks]
(c) Using the value of k found in (b):
(i) Find P⁻¹, the inverse of P. [4 marks]
(ii) Solve the matrix equation PX = [[11], [12]], where X is a 2×1 column matrix. [4 marks]

Question

Two matrices P and Q are defined as:
P = [[3, k], [2, 5]] and Q = [[1, -2], [0, 4]]
where k is a real constant.

(a) Find PQ in terms of k. [3 marks]
(b) Given that det(PQ) = 46, find the value of k. [4 marks]
(c) Using the value of k found in (b):
    (i) Find P⁻¹, the inverse of P. [4 marks]
    (ii) Solve the matrix equation PX = [[11], [12]], where X is a 2×1 column matrix. [4 marks]

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B) null

Answer

C) null

Answer

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