Singular matrix . It is the square matrix of order N whose determinant is null.
In this case, the system of linear equations associated with said matrix has no solution or has infinite matching solutions.
Summary
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- 1 Definitions
- 2 Examples
- 3 See also
- 4 Sources
Definitions
Given the square matrix A of order N, it is said to be a singular matrix when its determinant is zero.
Examples
In matrix A :
| one | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 | 9 |
When calculating its determinant:
- | A | = 1 (5×9-8×6) -4 (2×9-8×3) +7 (2×6-5×3) = 1 (45-48) -4 (18-24) +7 (12-15) = -3-4 (-6 ) +7 (-3) = -3 + 24-21 = 0,
it can be said that A is a singular matrix.
Instead the matrix M :
| one | 2 | 3 |
| 3 | 4 | 5 |
| 5 | 6 | 8 |
It has | M | = -2 , so it is non-singular.
