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

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Determinants of Matrices
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Determinant definition

A special value calculated from a square matrix

Notation for matrix determinant

det(A)\text{det}(A) or A|A|

Det. of (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}

adbcad - bc

3×3 det formula pattern

a(eifh)b(difg)+c(dheg)a(ei-fh) - b(di-fg) + c(dh-eg)

Singular matrix definition

Matrix with determinant equal to 0

Singular matrix inverse property

Does not have an inverse

Matrix invertibility condition

If and only if its determinant is non-zero

Determinant of identity matrix

Always 1

Effect of swapping two rows on det.

Changes the sign of the determinant

Effect of multiplying a row by scalar on det.

Multiplies the determinant by that scalar

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