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3 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2 · Question 6(b)(iii)

A nursery sells three brands of grass-seed mix, P, Q and R. Each brand is made from three types of grass, C, Z and B. The number of kilograms of each type of grass in a bag of each brand is summarised in the table provided. A blend is produced by mixing p bags of Brand P, q bags of Brand Q and r bags of Brand R.

Rewrite the set of THREE equations in (b)(ii) above in the matrix form MX = D where M is a 3 by 3 matrix, X and D are column matrices.

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  1. 6(a)(i)Find AB.[3 marks]
  2. 6(a)(ii)Deduce A^(-1).[3 marks]
  3. 6(b)(i)Write down an expression in terms of p, q and r, for the number of kilograms of Z-grass in the blend.[1 mark]
  4. 6(b)(ii)Let c, z and b represent the number of kilograms of C-grass, Z-grass and B-grass respectively in the blend. Write down a set of THREE equations in p, q, r, to…[3 marks]
  5. 6(b)(iv)Given that M^(-1) exists, write X in terms of M^(-1) and D.[3 marks]
  6. 6(b)(v)Given that M^(-1) = [[-0.2, -0.2, 0.3], [0.35, 0.1, -0.15], [-0.05, 0.2, -0.05]], calculate how many bags of EACH brand, P, Q, and R, are required to produce a…[4 marks]

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