Determinant of a diagonal matrix is equal to the
product of its main diagonal elements.
No common element is present between two diagonals of a
matrix of even order.
A (n+1)/2 is common element of two
diagonals o f a matrix of odd order n.
A2 is always symmetric for A being either symmetric
or skew-symmetric.
Non-homogenous system:
1.
A system is said to be consistent if its
solution exists otherwise inconsistent.
2.
If |A|=0 then solution does not exists.
3.
If |A|≠ 0 then solution exist.
4.
Solution exists if A is non-singular.
5.
Solution will exist if
a.
Rank of A = rank of Ab
6.
If rank of A = rank of Ab=
number of variables
a.
Then solution is unique.
7.
If rank of A = rank of Ab <
number of variables
a.
Then solutions are infinite.
Homogenous system:
1.
Every homogenous system has trivial or zero
solution.
2.
For non-trivial solution |A|=0
3.
If |A≠0 then non-trivial
solution does not exist.
Note:
In all above cases A is the matrix of co-efficient.
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