Inverses of Matrices (Edexcel A-Level Further Mathematics): Flashcards

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Inverses of Matrices
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Matrix that gives identity when multiplied by original

Inverse matrix

Condition for matrix to be invertible

Determinant is non-zero

Matrix with determinant zero

Singular matrix

Notation for inverse of matrix AA

A1A^{-1}

Inverse formula for 2×22 \times 2 matrix

1det(A)(dbca)\frac{1}{\text{det}(A)}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}

Matrix with 1s on diagonal, 0s elsewhere

Identity matrix

(AB)1(AB)^{-1} equals (order of inverses)

B1A1B^{-1}A^{-1} (order reversed)

Types of matrices that can have an inverse

Square matrices only

Solution to AX=BAX = B using inverse

X=A1BX = A^{-1}B

Transpose of cofactor matrix

Adjugate matrix

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