Exercise 506Linear algebra › Matrices and linear systemsHigh schoolAdded 3 Nov 2026

Determinant of a 3×3 matrix by Sarrus' rule

#determinant#Sarrus rule#3x3 matrices

Statement

Compute the determinant of
$A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10 \end{pmatrix}.$

Hint

Use Sarrus' rule: sum the three downward diagonals and subtract the three upward diagonals.

Show solutionHide solution

Solution

Sarrus' rule.
$\det A = 1\cdot5\cdot10 + 2\cdot6\cdot7 + 3\cdot4\cdot8 - 3\cdot5\cdot7 - 1\cdot6\cdot8 - 2\cdot4\cdot10.$
Compute:
$\det A = 50 + 84 + 96 - 105 - 48 - 80 = 230 - 233 = -3.$

Remark. The matrix is invertible since $\det A \neq 0$ .

Determinant of a 3×3 matrix by Sarrus' rule

Statement

Solution

More problems in Matrices and linear systems