Determinants

Warm up ,[object Object],[object Object],[object Object]

Sheets Matrices & Geometric Transformations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Finding the determinant of a matrix ,[object Object],[object Object],[object Object]

To find the determinant of a 2 x 2 matrix Example = (3)(2) - (4)(-1) = 6 + 4 = 10 3 -1 4 2

Finding the determinant of a 3 x 3 matrix using “expansion by minors” ,[object Object],[object Object],[object Object],= 3 0 3 4 1

Finding the determinant of a 3 x 3 matrix using “expansion by minors” ,[object Object],[object Object],[object Object],= 3 0 3 4 1 - 5 -2 3 1 1

Finding the determinant of a 3 x 3 matrix using “expansion by minors” = 3((0)(1)-(4)(3)) – 5((-2)(1)-(1)(3)) +-1((-2)(4)-(1)(0)) = 3(-12) – 5(-5) + -1(-8) = -36+25+8 = -3 ,[object Object],[object Object],[object Object],= 3 0 3 4 1 - 5 -2 3 1 1 + -1 -2 0 1 4 Note: Signs!

Finding the determinant of a 3 x 3 matrix using “diagonals” 3 -2 1 5 0 4 = (3 ·0 ·1 + 5 ·3 ·1 + -1 ·-2 ·4) - (-1 ·0 ·1 + 3 ·3 ·4 + 5 ·-2 ·1) = (0+15+8)-(0+36-10) =(23)-(26) = -3 ,[object Object],[object Object],[object Object]

Determinants

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Determinants