Matrices 1 (AQA A-Level Further Maths): Quizzes

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Systems of Linear Equations
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What is det(3425)\det\begin{pmatrix} 3 & 4 \\ 2 & 5 \end{pmatrix}?

77

A matrix AA is singular when which condition holds?

det(A)=0\det(A) = 0

Which matrices have an inverse?

Non-singular matrices only

If det(P)=3\det(P) = 3 and det(Q)=4\det(Q) = 4, what is det(PQ)\det(PQ)?

1212

What is the determinant of the identity matrix II?

11

In finding A1A^{-1}, which elements are swapped?

Leading diagonal elements

If det(A)=5\det(A) = 5, what is det(A1)\det(A^{-1})?

15\frac{1}{5}

If matrix CC is self-inverse, what are the possible values of det(C)\det(C)?

±1\pm 1

To solve Mx=bM\mathbf{x} = \mathbf{b}, which gives the solution?

x=M1b\mathbf{x} = M^{-1}\mathbf{b}

What is the inverse of product ABAB?

B1A1B^{-1}A^{-1}

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