Matrices 2 (AQA A-Level Further Maths): Quizzes

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Determinants, Inverse Matrices, and Linear Equations
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For matrix (5324)\begin{pmatrix} 5 & 3 \\ 2 & 4 \end{pmatrix}, what is the determinant?

1414

When finding a 3×3 determinant using the top row, what is the sign pattern?

Plus, minus, plus

What is the minor of an element in a matrix?

Det of 2×2 after removing its row & col

A shape with area 8 is transformed by matrix TT with det(T)=3\det(T) = -3. What is the image area?

2424

A cube is transformed by matrix MM where det(M)=5\det(M) = 5. The image volume is 40. What was original?

88

What does a negative determinant indicate about a transformation?

The transformation involves reflection

A matrix has det(A)=0\det(A) = 0. What can we conclude?

The matrix is singular, no inverse

For 2×2 matrix inverse, what is done to diagonal elements?

Swap them

System Mx=xMx = x' has unique solution when?

det(M)0\det(M) \neq 0

Three planes with det=0\det = 0 and no contradictions means?

Infinite solutions along a line

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