Edexcel FP3 — Question 19

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
Topic3x3 Matrices

19. $$\mathbf { A } = \left( \begin{array} { r r r } 3 & 1 & - 1
1 & 1 & 1
5 & 3 & u \end{array} \right) , \quad u \neq 1$$
  1. Show that \(\operatorname { det } \mathbf { A } = 2 ( u - 1 )\).
  2. Find the inverse of \(\mathbf { A }\). The image of the vector \(\left( \begin{array} { l } a
    b
    c \end{array} \right)\) when transformed by the matrix \(\left( \begin{array} { r r r } 3 & 1 & - 1
    1 & 1 & 1
    5 & 3 & 6 \end{array} \right)\) is \(\left( \begin{array} { l } 3
    1
    6 \end{array} \right)\).
  3. Find the values of \(a , b\) and \(c\).
    (3)
    [0pt] [P6 June 2003 Qn 6]