ECZ 2011 · O-Level Paper 2 · Question 2 — Matrices

Question from ECZ 2011 · O-Level Paper 2 · Question 2

(a) Express x + 23 - 2x - 34 as a single fraction in its simplest form.[3]

Verified working — step 1

The lowest common denominator of 3 and 4 is 12.

(b) Given that matrix A = 1x-12,

(b(i)) write an expression in terms of x, for the determinant of A,[1]

Verified working — step 1

A = 1x-12.

(b(ii)) find the value of x, given that the determinant of A is 5,[2]

Verified working — step 1

Set the determinant equal to 5.

(b(iii)) write A^-1.[1]

Verified working — step 1

With x = 3, A = 13-12 and det A = 5.

(c) Solve the equation 12x + 2 = 35.[2]

Verified working — step 1

Cross-multiply to clear the fractions.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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