Determinant of a singular 3×3 matrix
The determinant of the singular 3×3 matrix with rows (1, 2, 3), (4, 5, 6), (7, 8, 9) is 0. See the full step-by-step working and edit the matrix to try your own.
The 3x3 matrix with rows (1, 2, 3), (4, 5, 6), (7, 8, 9) has determinant 0. The calculator below is loaded with it, so you can follow every step or edit the entries.
Why the answer is 0
Row 3 minus row 2 equals row 2 minus row 1, so the rows are dependent and the determinant vanishes.
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Frequently asked questions
What is the determinant of this singular 3×3 matrix? ▾
It is 0. Row 3 minus row 2 equals row 2 minus row 1, so the rows are dependent and the determinant vanishes.
Why is this determinant zero? ▾
A zero determinant means the rows are linearly dependent, so the matrix collapses space into a lower dimension and cannot be inverted.
Can I change the numbers? ▾
Yes — the calculator above is fully editable. Type over any entry and the determinant and every step recalculate immediately.
About this Calculator
The determinant of the singular 3×3 matrix with rows (1, 2, 3), (4, 5, 6), (7, 8, 9) is 0. See the full step-by-step working and edit the matrix to try your own.