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What is a matrix ?What is a matrix ?
ELEMENTS ARRANGED IN ROWS ANDELEMENTS ARRANGED IN ROWS AND COLUMNS AND CLOSED IN BRACKETCOLUMNS AND CLOSED IN BRACKET
IS CALLED A MATRIX.IS CALLED A MATRIX.
Example of MatrixExample of Matrix
[ ] [ ] The above is the matrix The above is the matrix
with 2X3 like-wise there can be any type with 2X3 like-wise there can be any type of Matrix with any combinationof Matrix with any combination
2 3 4
5 6 6
mmx x nn MATRIXMATRIX
A matrix has A matrix has m m rowsrows and and n n
columnscolumns is is called an m called an m x x
n matrix.n matrix.
ORDER OF THE MATRIXORDER OF THE MATRIX
4 5 64 5 6 IN THIS MATRIX THERE ARE 2 IN THIS MATRIX THERE ARE 2 ROWS , 3 COLUMNS, SO IT’SROWS , 3 COLUMNS, SO IT’S
7 8 97 8 9 CALLED AS 2x3 MATRIXCALLED AS 2x3 MATRIX
2 3 2 3 IN THIS MATRIX THERE ARE 3 ROWS IN THIS MATRIX THERE ARE 3 ROWS
2 COLUMNS, SO IT’S CALLED AS 3x2 2 COLUMNS, SO IT’S CALLED AS 3x2 MATRIXMATRIX
4 54 5
6 76 7
ROWROW
MATRIXMATRIXElementsElements arrangedarranged inin
aa singlesingle rowrow isis calledcalled asas
rowrow matrixmatrix..
3 5 83 5 8
COLUMN COLUMN MATRIXMATRIX
74
NULLNULL MATRIXMATRIX• A MATRIX WHICH HAS A MATRIX WHICH HAS 0 S0 S AS AS
ELEMENTS IS CALLEDELEMENTS IS CALLED ASAS NULLMATRIX.NULLMATRIX.
0 00 0 0 00 0
SQUARESQUARE MATRIXMATRIX
A matrix has equal rows and columns A matrix has equal rows and columns is called a square matrix.is called a square matrix.
3 1 9 This matrix has 3 rows3 1 9 This matrix has 3 rows
6 0 5 and 3 columns so it is 6 0 5 and 3 columns so it is
8 7 4 called as square matrix.8 7 4 called as square matrix.
RECTANGULAR MATRIXRECTANGULAR MATRIX
A matrix having different rows and A matrix having different rows and columns in number is called columns in number is called rectangular matrix.rectangular matrix.
4 5 6
2 7 -72 X 3
TRANSPOSE OF AMATRIXTRANSPOSE OF AMATRIX
• Exchange the rows as columns, and Exchange the rows as columns, and columns as rows we get the transpose of a columns as rows we get the transpose of a
matrix.matrix.
2 5 7
4 6 9A =
2 4
5 6
7 9
AT
=