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3 marksMatrices and Systems of Linear Equations

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

A system of equations is given by \begin{aligned} x - y + z &= 1 \\ x - 2y + 4z &= 5 \\ x + 3y + 9z &= 25. \end{aligned}

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.

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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)(i)b)Hence deduce the inverse \mathbf{A}^{-1} of the matrix \mathbf{A}.[3 marks]
  4. 6(b)(ii)b)Hence, or otherwise, solve the system of equations.[5 marks]

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