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7 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 6(b)(ii)

Given A = \begin{pmatrix} 0 & -1 & 1 \\ -1 & 0 & 1 \\ 1 & 1 & 1 \end{pmatrix}.

Find the values of k for which |kI - A| = 0.

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Other parts of this question

  1. 6(a)(i)Write the system in matrix form.[1 mark]
  2. 6(a)(ii)Write down the augmented matrix.[1 mark]
  3. 6(a)(iii)Reduce the augmented matrix to echelon form.[3 marks]
  4. 6(a)(iv)Deduce the value of \alpha for which the system is consistent.[1 mark]
  5. 6(a)(v)Find ALL solutions corresponding to this value of \alpha.[4 marks]
  6. 6(b)(i)Find kI - A, where I is the 3 \times 3 identity matrix and k is a real number.[3 marks]

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