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3 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2 · Question 5(c)(i)

Let A = \begin{pmatrix} 1 & 0 & 3 \\ 2 & 1 & -1 \\ 1 & -1 & 1 \end{pmatrix}.

Find the matrix \mathbf{B}, where \mathbf{B} = \mathbf{A}^2 - 3\mathbf{A} - \mathbf{I}.

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Other parts of this question

  1. 5(a)(i)Determine how many such numbers can be formed if each digit appears at most once.[4 marks]
  2. 5(a)(ii)Determine how many such numbers can be formed if there is no restriction on the number of times a digit may appear.[3 marks]
  3. 5(b)(i)Find the probability that the committee consists entirely of Jamaicans.[3 marks]
  4. 5(b)(ii)Find the number of ways in which the committee can be formed, given the restriction that there are as many Tobagonians on the committee as there are Guyanese.[6 marks]
  5. 5(c)(ii)Show that \mathbf{AB} = -9\mathbf{I}.[1 mark]
  6. 5(c)(iii)Hence, find the inverse, \mathbf{A}^{-1}, of \mathbf{A}.[2 marks]
  7. 5(c)(iv)Solve the system of linear equations \mathbf{B} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}.[3 marks]

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