Matrix Determinant - Tutorial

Matrix Determinant - Tutorial

Determinant of Matrix :

The determinant of a square matrix is a single number calculated by combining all the elements of the matrix. Determinant of a matrix A is denoted by |A|. The Equation or Formula is calcuated as

Equation to calculate the determinant of 2x2 Matrix
|A| =
a1b1
a2b2
= a1xb2 - a2xb1
Equation to calculate the determinant of 3x3 Matrix
|A| =
a1b1c1
a2b2c2
a3b3c3
=
a1b1c1
a2b2c2
a3b3c3
-
a1b1c1
a2b2c2
a3b3c3
+
a1b1c1
a2b2c2
a3b3c3

The expansion of the determinant is.

|A| =
a1b1c1
a2b2c2
a3b3c3
= a1
b2c2
b3c3
- b1
a2c2
a3c3
+ c1
a2b2
a3b3
so |A| = A = a1(b2c3-c2b3) - b1(a2c3-c2a3) + c1(a2b3-b2a3)

Thus we have to use the above formulas to calculate the value of determinant of the matrices. Note: We can calculate the inverse of a matrix only when the determinant of that matrix is not equal to zero.

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