CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2 · Question 6(a)(i)
The matrix A = \begin{pmatrix} 1 & 1 & 1 \\ 2 & -3 & 2 \\ -1 & -3 & -2 \end{pmatrix}.
Show that |A| = 5.
The mark scheme is shown once you've answered.
Practise this questionOther parts of this question
- 6(a)(ii) a)Matrix B is formed by interchanging row 1 and row 2 of matrix A and then interchanging column 1 and column 2 of the resulting matrix. Write down det(B), giving…[2 marks]
- 6(a)(ii) b)Row 1 of matrix C is formed by adding row 2 to row 1 of matrix A. The other rows remain unchanged. Write down det(C), giving a reason.[2 marks]
- 6(a)(ii) c)Matrix D is formed by multiplying each element of matrix A by 5. Write down det(D), giving a reason.[2 marks]
- 6(b)(i)Find AM.[3 marks]
- 6(b)(ii)Find the inverse, A^{-1}, of A.[2 marks]
- 6(c)(i)Write the system of equations in the form Ax = b.[1 mark]
- 6(c)(ii)Show that x = A^{-1}b.[2 marks]
- 6(c)(iii)Hence, solve the system of equations.[2 marks]
- 6(c)(iv) a)Show that (x, y, z) = (1, 1, 1) is a solution of the system of equations: x + y + z = 3 2x + 2y + 2z = 6 3x + 3y + 3z = 9.[1 mark]
- 6(c)(iv) b)Hence, find the general solution of the system.[5 marks]
More practice: the rest of this paper · more Matrices and Systems of Linear Equations questions · all CAPE Pure Mathematics Unit 2 past papers