Pearson Edexcel IAL Mathematics FP1.5.4 Evaluation of 2 × 2 determinants

Practise evaluating 2 x 2 determinants, using det M to decide singularity and solve for constants in matrix questions.

Exam points

find det M using ad-bc and simplify expressions involving constants
set a determinant to zero to find when a matrix is singular

[Maximum number: 3]

$\mathbf M=\left(\text{row }1:2k+1,\ k;\ \text{row }2:k+7,\ k+4\right),$
where k is a constant.

Show that M is non-singular for all real values of k.

$\det\mathbf M=(2k+1)(k+4)-k(k+7)=k^2+2k+4.$
M1

$k^2+2k+4=(k+1)^2+3>0$
for all real k. M1

Therefore $\det\mathbf M\neq 0$ , so $\mathbf M$ is non-singular for all real k. A1

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FP1.5.4 - Evaluation of 2 × 2 determinants question 1