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|
=
.
a1
b1
a2
b2
.
=
a1xb2 - a2xb1
Equation to calculate the determinant of 3x3 Matrix
|A|
=
.
a1
b1
c1
a2
b2
c2
a3
b3
c3
.
=
a1
b1
c1
a2
b2
c2
a3
b3
c3
-
a1
b1
c1
a2
b2
c2
a3
b3
c3
+
a1
b1
c1
a2
b2
c2
a3
b3
c3
The expansion of the determinant is..
|A|
=
.
a1
b1
c1
a2
b2
c2
a3
b3
c3
.
=
a1
.
b2
c2
b3
c3
.
- b1
.
a2
c2
a3
c3
.
+ c1
.
a2
b2
a3
b3
.
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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