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Matrices
1.
2. It is an collection of elements which is arranges in
rows columns.
It is the Combination of linear equation.
It is Represented by these symbols:
, ,
e.g. -
3*3
3. 1. Row matrices – A matrices which has only one row
called row matrices e.g.-
[123]1*3
2. Column matrices – A matrices which has only one
column is called column matrices e.g. –
4. 3. Square matrices – No. of the rows and No. of the
column is same e.g.
4. Null matrices – Which all elements is equal to ‘0’
5. 5. Identity matrices – A square matrices who’s main
diagonal is assinty value ‘1’ and each of the other
element is ‘0’ e.g. -
6. Diagonal matrices – A square matrices all of who’s
element expect those in the leading diagonal are ‘0’
e.g. -
,
6. 7. Scalar matrices – A diagonal matrices in which all the
elements of main diagonal is same called scalar
matrices e.g.-
8. Triangular matrices – there are two types: -
Upper triangular – All the below elements are ‘0’
Lower triangular – All the above elements are ‘0’
3*3
7. 9. Transpose Matrices – A matrices obtained by inter
changing the rows and columns of a matrices A
It is
denoted by A’ , AT e.g.:-
10. Symmetric Matrices - A square matrices A is called
symmetric matrices if it is equal to its transpose e.g.-
A AT
8. 11. Skew Matrices - if A’ = -A is called skew matrices
e.g.-
12. Equal Matrices – If two matrices order and there
corresponding element is same is called equal
matrices
2*2
If X
9. 13. Algebraic Matrices – There are three type:-
i. Addition method - for addition of two matrices the
order must be same e.g.:-
A
+
10. ii. Subtraction method –For subtraction of two matrices
the order must be same.
Example:-
A
A-B