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3 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2 · Question 6(b)(i)b)

Given the matrices \mathbf{A} = \begin{pmatrix} 1 & -1 & 1 \\ 1 & -2 & 4 \\ 1 & 3 & 9 \end{pmatrix} and \mathbf{B} = \begin{pmatrix} 30 & -12 & 2 \\ 5 & -8 & 3 \\ -5 & 4 & 1 \end{pmatrix}.

Hence deduce the inverse \mathbf{A}^{-1} of the matrix \mathbf{A}.

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Other parts of this question

  1. 6(a)Solve for x the equation \begin{vmatrix} x - 3 & 1 & -1 \\ 1 & x - 5 & 1 \\ -1 & 1 & x - 3 \end{vmatrix} = 0.[10 marks]
  2. 6(b)(i)a)Find \mathbf{A}\mathbf{B}.[4 marks]
  3. 6(b)(ii)a)Express the system in the form \mathbf{A}\mathbf{x} = \mathbf{b}, where \mathbf{A} is a matrix and \mathbf{x} and \mathbf{b} are column vectors.[3 marks]
  4. 6(b)(ii)b)Hence, or otherwise, solve the system of equations.[5 marks]

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