Civil Engineering Reference
In-Depth Information
Example 2.4
Cramer's rule
Find the solution set to the following non-homogeneous linear algebraic
equations using Cramer's rule.
282 4
6
xxx
xxx
xx x
++=
+−=
−+ =
1
2
3
13
1
2
3
2
2
5
1
2
3
282
16 1
212
A
=
−
=−
36
−
14 82
13 61
512
A
=
−
=−
180
1
−
2142
1131
252
A
=
− =−
36
2
2814
1613
215
A
=
=
72
3
−
A
A
x
===
−
−
180
36
1
=
5
1
A
A
==
−
−
36
36
2
x
=
1
2
A
A
72
36
3
x
==
−
=−
2
3
The determinants are shown by row expansion in Table 2.1.
2.5
MEtHOD Of ADJOintS OR cOfActOR
MEtHOD
The solution to a set of linear algebraic equations can be achieved by using
the invert of a matrix. The cofactor and adjoint matrices are very helpful
in finding this invert by utilizing determinants.The
cofactor matrix
is one
where the elements of the matrix are cofactors. Each term in the cofactor
