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3 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2 · Question 5(b)(i)b)

Given the matrices A = \begin{pmatrix} 3 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & -1 & 0 \end{pmatrix}, B = \begin{pmatrix} 1 & -1 & 1 \\ 0 & 0 & -1 \\ -1 & 3 & -1 \end{pmatrix} and M = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 0 & -3 \\ -1 & 3 & -1 \end{pmatrix}.

Determine the matrix AM.

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Other parts of this question

  1. 5(a)(i)In how many ways can this committee be selected so that the committee includes AT LEAST ONE former batsman?[8 marks]
  2. 5(a)(ii)In how many ways can this committee be selected so that the committee includes AT LEAST ONE batsman and ONE bowler?[3 marks]
  3. 5(b)(i)a)Determine the matrix A - B.[2 marks]
  4. 5(b)(ii)Deduce from (i) b) above the inverse A^{-1} of the matrix A.[3 marks]
  5. 5(b)(iii)Find the matrix X such that AX + B = A.[6 marks]

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