Vectors and matrices — Question 12
QCAA 2023, Paper 1 · 5 marks
Q12 · 2023 · Technology-freeSimple familiar5 marks
QUESTION 12 (5 marks)
Given A=(11−22), B=(0123) and C=(−10−13), determine X in the matrix equation XA−XC=B. WORKED SOLUTION
QCAA guide · typeset solution
5 marksANSWERX=(24−4−7). Worked solution
XA−XC=X(A−C)=B, so
X=B(A−C)−1.
Here
A−C=(21−1−1),
and evaluating the inverse and product gives
X=(24−4−7). recognises the need for X as a common factor [1 mark]expresses X as the subject [1 mark]represents X in terms of two matrices [1 mark]calculates the inverse of the appropriate matrix
[1 mark]One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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