Decomposition by:
Number format
Solution comments
Without description (answer only)
a
b
c
d
x
y
z
clear
i
Randomize
3131313131351515151515≈83137
How to find the determinant by the Sarrus rule
The Sarrus rule is a mnemonic for computing the determinant of a 3×3 matrix. Write the first two columns to the right of the matrix, then sum the products of the three left-to-right diagonals and subtract the products of the three right-to-left diagonals. The rule does not extend to matrices larger than 3×3.
Sarrus rule worked example (3×3)
Write the initial matrix
A
:
A
=
3
0
1
1
4
0
2
5
6
To find the determinant of matrix
A
need to do the following:
1)
To the right of matrix A, we add the first two columns;2)
Take the products of the elements on the main diagonal and on the diagonals parallel to it with a plus sign;3)
Take the products of the elements of the secondary diagonal and diagonals parallel to it with a minus sign;det(
A
) =
a
0
1,1
·
a
0
2,2
·
a
0
3,3
+
a
0
1,2
·
a
0
2,3
·
a
0
3,1
+
a
0
1,3
·
a
0
2,1
·
a
0
3,2
−
a
0
1,3
·
a
0
2,2
·
a
0
3,1
−
a
0
1,1
·
a
0
2,3
·
a
0
3,2
−
a
0
1,2
·
a
0
2,1
·
a
0
3,3
a
a is an element of matrix A;To the right of matrix
A
, we add the first two columns;
3
0
1
1
4
0
2
5
6
3
0
1
1
4
0
Take the products of the elements on the main diagonal and on the diagonals parallel to it with a plus sign;
= (
a
0
1,1
*
a
0
2,2
*
a
0
3,3
) + (
a
0
1,2
*
a
0
2,3
*
a
0
3,1
) + (
a
0
1,3
*
a
0
2,1
*
a
0
3,2
) -
Take the products of the elements of the secondary diagonal and diagonals parallel to it with a minus sign;
- (
a
0
1,3
*
a
0
2,2
*
a
0
3,1
) - (
a
0
1,1
*
a
0
2,3
*
a
0
3,2
) - (
a
0
1,2
*
a
0
2,1
*
a
0
3,3
) =
= (
3
*
4
*
6
) + (
1
*
5
*
1
) + (
2
*
0
*
0
) -
- (
2
*
4
*
1
) - (
3
*
5
*
0
) - (
1
*
0
*
6
) =
69
;
Answer
det(A)det(
A
) =
69
;
SIZE3×3METHODSarrus