3x3 matrix determinant calculator
Expanding along the first row turns a 3x3 determinant into three 2x2 ones.
Determinant
-306
- First minor
- -54
- Second minor
- 18
- Third minor
- 36
- Trace
- 11
- Singular
- 0
Show the working
- Row 1, column 1 = 6
- Row 1, column 2 = 1
- Row 1, column 3 = 1
- Row 2, column 1 = 4
- Row 2, column 2 = -2
- Row 2, column 3 = 5
- Row 3, column 1 = 2
- Row 3, column 2 = 8
- Row 3, column 3 = 7
- First minor = -2*7 - 5*8 = -54
- Second minor = 4*7 - 5*2 = 18
- Third minor = 4*8 - -2*2 = 36
- Determinant = 6*-54 - 1*18 + 1*36 = -306
- Trace = 6 + -2 + 7 = 11
- Singular = -306 == 0 ? 1 : 0 = 0
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- det = a11(a22 a33 - a23 a32) - a12(a21 a33 - a23 a31) + a13(a21 a32 - a22 a31)