Previously we have discussed about qualitative solution and In the study of discrete maths, we find that the knowledge of matrices is very important and it is the powerful tool which has variety of applications in our life and its an important part of CBSE math Syllabus. It just simplifies so many calculations.All problems related to solving linear equations can be easily solved by use of Matrices and determinants.
Now let us first see what is Matrix? Matrix is a rectangular Array of m * n numbers in the form of m rows ( which are vertical lines ) and n columns, (which are horizontal lines). The matrix is called m x n ( m by n matrix ). We always enclose an array by [ ] or ( ). The number of elements of the matrix are m*n. This is called the order of any particular Matrix. If we talk of more than one matrix, we say matrices. So word matrices is plural of Matrix.
3 5 7
2 3 6 is the matrix of 2 rows and 3 columns, so it is 2 x 3 matrix
To find the location of a particular element of the matrix, we simply mention the row and column of which the element is taken. Lets say 3 is the ( 1, 2 )th element of the given matrix. Each element is represented as a(ij) , where I and j are the respective rows and columns.(Want to know more about discrete mathematics,Click here)
Let us see an example. If there is a matrix of 12 elements, what are the possible orders of that matrix?
All possible orders of the matrix with 12 elements are ( 1, 12 ) , ( 2, 6 ), ( 3, 4 ), ( 4, 3 ), ( 6, 2 ), (12 , 1 ).
If we have to construct a 3 x 2 matrix, whose elements are given by
aij = ( I + 2j ) .
Then , we first observe that the matrix is 3 x 2 , it means it has 2 rows and 3 columns. So the value of I = 1 , 2 , 3 and value of j = 1, 2 .
So a11 = ( 1 + 2 * 1) = 1 + 2 = 3; a12 =( 1 + 2 *2 ) = 1 + 4 = 5
a21 = ( 2 + 2 * 1 ) = 2 + 2 = 4 ; a22 = ( 2 + 2 * 2) = 2 + 4 = 6
a31 = ( 3 + 2 * 1 ) = 3 + 2 = 5 ; a32 = ( 3 + 2 * 2 ) = 3 + 4 = 7
so we get the matrix: A = 3 4
4 6
5 7
We should always remember that a matrix is always represented by capital letter.
Scalar Matrix: A matrix where every non – diagonal element is zero and the diagonal elements are equal are called scalar matrix.
5 0 0
0 5 0 is the scalar matrix of order 3.
0 0 5
Unit Matrix: A matrix in which all non- diagonal elements are zero and the diagonal element is “ 1” is called a unit matrix.
1 0 is the unit matrix of order 2
0 1
and
1 0 0
0 1 0 the unit matrix of order 3.
0 0 1
This is all about Discrete Mathematics and if anyone want to know about Compound Statements then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Congruence and Similarity in the next session here.
Now let us first see what is Matrix? Matrix is a rectangular Array of m * n numbers in the form of m rows ( which are vertical lines ) and n columns, (which are horizontal lines). The matrix is called m x n ( m by n matrix ). We always enclose an array by [ ] or ( ). The number of elements of the matrix are m*n. This is called the order of any particular Matrix. If we talk of more than one matrix, we say matrices. So word matrices is plural of Matrix.
3 5 7
2 3 6 is the matrix of 2 rows and 3 columns, so it is 2 x 3 matrix
To find the location of a particular element of the matrix, we simply mention the row and column of which the element is taken. Lets say 3 is the ( 1, 2 )th element of the given matrix. Each element is represented as a(ij) , where I and j are the respective rows and columns.(Want to know more about discrete mathematics,Click here)
Let us see an example. If there is a matrix of 12 elements, what are the possible orders of that matrix?
All possible orders of the matrix with 12 elements are ( 1, 12 ) , ( 2, 6 ), ( 3, 4 ), ( 4, 3 ), ( 6, 2 ), (12 , 1 ).
If we have to construct a 3 x 2 matrix, whose elements are given by
aij = ( I + 2j ) .
Then , we first observe that the matrix is 3 x 2 , it means it has 2 rows and 3 columns. So the value of I = 1 , 2 , 3 and value of j = 1, 2 .
So a11 = ( 1 + 2 * 1) = 1 + 2 = 3; a12 =( 1 + 2 *2 ) = 1 + 4 = 5
a21 = ( 2 + 2 * 1 ) = 2 + 2 = 4 ; a22 = ( 2 + 2 * 2) = 2 + 4 = 6
a31 = ( 3 + 2 * 1 ) = 3 + 2 = 5 ; a32 = ( 3 + 2 * 2 ) = 3 + 4 = 7
so we get the matrix: A = 3 4
4 6
5 7
We should always remember that a matrix is always represented by capital letter.
Scalar Matrix: A matrix where every non – diagonal element is zero and the diagonal elements are equal are called scalar matrix.
5 0 0
0 5 0 is the scalar matrix of order 3.
0 0 5
Unit Matrix: A matrix in which all non- diagonal elements are zero and the diagonal element is “ 1” is called a unit matrix.
1 0 is the unit matrix of order 2
0 1
and
1 0 0
0 1 0 the unit matrix of order 3.
0 0 1
This is all about Discrete Mathematics and if anyone want to know about Compound Statements then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Congruence and Similarity in the next session here.
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