Matrices and determinants are very nice ways to vepresent bunch of number. matrices as well as determinants dlong with some very nice properties that each of then have, prove to be very useful in solving equations, finding area of polygons etc. Matrices a also find use in Linear Algebra which is beyond the scope of JEE syllabus.
So, Let us study these in details.
Matrices And Determinants
MATRICES
A rectangular away of elements or symbols.along sows and wlumns in colled a matricx .
Equal MAtrices :- Two matrices are eqnal if they have the same order and each element of ove is equal to the corresponding of the other.
Classification (Secondaty Information):-
Row Matrix
A mstrix lhaving a single row .
Column Matrix
A matrix with a single column .
Square Matrix
An m X n matrix is said to be a square matrix if m = n i.e. no. of rows = no. o of columns.
eg: A -
Trace of a Matrix
The sum of the elements of O square matrix A lying along the principal diagonal .
Properties of trace of a matrix(Secondary Information) :-
(i) tr (
A) =
tr (A)
(ii) tr (A + B) = tr (A) + tr (B)
(iii) tr (A B) = tr (B A)
Diagonal Matrix (Secondary Information) :-
A square matrix with all the elemente O except the diagonal elements.
Scalar Matrix:- A diagonal matrix whose all the leading elements are equal.
Unit or Identify Matrix:-
A diagonal matrix of order n which has only unity for all its diagonal elements. is called unit or Identify matrix of order n and is denoted by In.
Triangnlar Matrix (Secondary Information):
A square matrix in which all the elements below the diagonal are zero is called upper triangnlar and square matrix in which all the elements above diagonal are zero is called lower triangnlar matrix .