MATRICES ICSE
Posted by sreeram sudha on July 5, 2010
Matrices is an interesting topic in the field of Mathematics. A matrix is a rectangular arrangement of numbers , as horizontal rows and vertical columns , similar to the arrangement of elements in the Periodic Table . So each number of the matrix can be called as an element of the Matrix.
If the number of Rows in a matrix ( A ) is m and the number of Columns is n , then the said Matrix is of the Order m X n and is written as A = (aij)
There are different types of Matrices , like
1) Equal matrix : Two matrices are called as Equal matrices only if they are of the same order and their corresponding elements are equal.
2) Row Matrix : Has only one Row of elements.
3) Column matrix : Has only one Column of Elements.
4) Square matrix : The number of Rows and Columns are equal.
5)Zero or Null Matrix : Each element is Zero.
6) Diagonal matrix : All elements except the elements in the main Diagonal are
Zero..
7) Unit matrix : Each of its diagonal element is 1 and each of all other
or Elements is zero.
(Identity Matrix)
Addition and Subtraction of matrices :
Two matrices of the same order are added by adding their corresponding elements. The element in the 1st row and 1st column of the first matrix is to be added with the element in the first row and first column of the second matrix and placed in the 1st row and 1st column of the newly formed matrix..
Similarly , the other elements of the first Matrix are added to thier corresponding elements in the second matrix .
For example A and B are two matrices of the same order , then
A+B=B+A
But A-B is not equal to B-A
This is an important fact the student has to remember while working sums on Matrices.
Multiplication of Matrices :
The product AB of two matrices A and B is possible only when the number of columns in A is equal to the number of rows in B .
A is called the pre-multplier and B is called the post multiplier.
The student can follow the following steps while finding the product of two matrices A and B.
1) First multiply the elements of the 1st row of A by the corresponding elements of the 1st column of B and add. The number got after adding becomes the 1st element in the 1st row of the resulting matrix. AB
2)Multiply the elements of the 1st row of A by the corresponding elements of the 2nd column of B and add. This becomes the second element in the first row of the resulting matrix AB.
3)In the same manner , the remaining elements of the first row of the resulting matrix AB can be obtained.
4) Proceeding in the same way , the student can get the elements of the remaining rows of the resulting matrix. AB .
Transpose of a Matrix is another interesting fact about a matrix.
The transpose of a matrix A is A^T .The elements in A^T can be obtained by interchanging the rows and columns of the given matrix.
For example A = 1 2
5 9
then A^T = 1 5
2 9
Important fact about multiplication of Matrices :
If the order of matrix A is m X n and the order of matrix B is n X p then the product AB is possible and the order of the product matrix obtained is m X p , i.e number of rows of matrix A X number of columns of matrix B .
