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4 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2 · Question 5(b)(i)

Matrices A and B are given by A = \begin{pmatrix} 1 & x & -1 \\ 3 & 0 & 2 \\ 2 & 1 & 0 \end{pmatrix} and B = \begin{pmatrix} 1 & 2 & 5 \\ 2 & 3 & 4 \\ 1 & 1 & 2 \end{pmatrix}.

Determine the range of values of x for which A^{-1} exists.

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Other parts of this question

  1. 5(a)(i)Five teams are to meet at a round table. Each team consists of two members AND one leader. How many seating arrangements are possible if each team sits…[7 marks]
  2. 5(a)(ii)a)Given that 40% of the individuals used red and 50% used blue, calculate the probability that an individual used BOTH colours.[4 marks]
  3. 5(a)(ii)b)Determine the TOTAL number of individuals that participated in the experiment.[2 marks]
  4. 5(b)(ii)Given that \det(AB) = -21, show that x = 3.[4 marks]
  5. 5(b)(iii)Hence, obtain A^{-1}.[4 marks]

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