Determinant calculation

Questions asking to find the determinant of a given matrix, possibly in terms of parameters.

4 questions · Moderate -0.7

4.03h Determinant 2x2: calculation
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Edexcel FP1 2013 June Q1
5 marks Moderate -0.8
\(\mathbf { M } = \left( \begin{array} { c c } a & 1 \\ 1 & 2 - a \end{array} \right)\), where \(a\) is a constant.
  1. Find det M in terms of \(a\).
    (2) A triangle \(T\) is transformed to \(T ^ { \prime }\) by the matrix M .
    Given that the area of \(T ^ { \prime }\) is 0 ,
  2. find the value of \(a\).
    (3)
Edexcel F1 2022 January Q1
5 marks Moderate -0.3
$$\mathbf{M} = \begin{pmatrix} 3x & 7 \\ 4x + 1 & 2 - x \end{pmatrix}$$ Find the range of values of \(x\) for which the determinant of the matrix \(\mathbf{M}\) is positive. [5]
AQA Further AS Paper 1 2018 June Q12
6 marks Standard +0.3
  1. Show that the matrix \(\begin{pmatrix} 5 - k & 2 \\ k^3 + 1 & k \end{pmatrix}\) is singular when \(k = 1\). [1 mark]
  2. Find the values of \(k\) for which the matrix \(\begin{pmatrix} 5 - k & 2 \\ k^3 + 1 & k \end{pmatrix}\) has a negative determinant. Fully justify your answer. [5 marks]
AQA Further AS Paper 1 2019 June Q2
1 marks Easy -1.8
Which of the following expressions is the determinant of the matrix \(\begin{bmatrix} a & 2 \\ b & 5 \end{bmatrix}\)? Circle your answer. [1 mark] \(5a - 2b\) \quad \(2a - 5b\) \quad \(5b - 2a\) \quad \(2b - 5a\)