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

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Determinants, Inverse Matrices, and Linear Equations
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Det. of (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}

adbcad - bc

Minor of a matrix element

Det. after removing element's row and column

Sign pattern for 3×3 det. using top row

Plus, minus, plus

Area of image under transformation T\mathbf{T}

Area of original × det(T)|\det(\mathbf{T})|

What negative determinant indicates

Reflection in the transformation

Condition for matrix to have an inverse

det(A)0\det(\mathbf{A}) \neq 0 (non-singular)

Steps to find 2×2 inverse

Swap diagonals, change signs of off-diagonals, ÷ by det.

Sign matrix for 3×3 inverse (checkerboard pattern)

(+++++)\begin{pmatrix} + & - & + \\ - & + & - \\ + & - & + \end{pmatrix}

Condition for unique solution to Mx=x\mathbf{M}\mathbf{x} = \mathbf{x}'

det(M)0\det(\mathbf{M}) \neq 0

If det(M)=0\det(\mathbf{M}) = 0 in linear system

No solution or infinitely many solutions

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