Matrix

1.What is the Matrix: Matrix is a rectangular arrangement of numbers, arranged in horizontal rows and vertical columns. Plural of matrix is matrices. e.g. |1,2,3| |1,21 14,5,61 14,51 17,8,91 11,2,3| 17,8] Note: 1. Each entity or number in a matrix is called an element. 2. In any matrix Horizontal lines are called rows while the vertical lines are called columns.

2.What is the order of Matrix: If a matrix has columns and rows, then the order is written as. 11,2,3| 14,5,6| So for example in 7,8,9| m-3 and n=3. Hence or der= 3x3 Matrices are normaly denoted by capital letters.If A is a matrix with M rows and n columns, then it is denoted as A mXn 3.What is the type of Matrices: Row Matrix: This is a matrix, that has only one row. e.g. 11,2,3|

|1|

|2|

Column Matrix: This is a matrix, that has only one column. e.g. |3| Square Matrix: This is a matrix where the numbers of rows are equal to number of columns. e.g. |1,2,3| 14,5,6| 17,8,9| Rectangular Matrix: This is a matrix where the numbers of rows are not equal to number of columns. e.g. |1,2,3,4|| 14,5,6,7|| |7,8,9,10| Zero or Null Matrix: If each element of a matrix is 0, then it is called Zero or 10| 10,0,0,0|| 10| 10,0,0,0|| Null Matrix. e.g. 10,0,0| 101 10,0,0,0|| Diagonal Matrix: This is a square matrix, where all elements are 0 except the |1,0,0|| 10,5,0| ones on the leading diagonal. e.g. 10,0,9||

Unit or Identity Matrix: A diagonal matrix, where each element of the leading |1,0,0|| 10,1,0|| |1,0|| diagonal is 1 is called Unit or Identity matrix. e.g. |0,0,1| 10,1||

4.What is the Identity Matrix: O is called the additive identity of any number because the number does not change. Similarly, there is an additive identity of a matrix as well. If a matrix is added to a null matrix of the same order, the matrix remains unchanged. Hence the null matrix of the same order is called the Additive Identity of the matrix. e.g. |1,2|| 10,0| |1+0 2+0| |1,2| 13,4| + 10,0| = 13+0 4+0| = 13,4|| 5. What is the Addition of Matrix: Two matrices can be added only if the order of the two matrices is the same. To add two matrices of the same order, just add the corresponding terms, e.g. |1,2| 15,6| |1+5 2+6| 16 ,8|| |3,4| + 17,8| = 13+7 4+8| = |10,12|

6. What is the Subtraction of Matrix: Two matrices can be subtracted only if the order of the two matrices is the same. To subtract two matrices of the same order, just subtract the corresponding terms. e.g. |1,2| 15,6| |1-5,2-6| |-4,-4| 13,4| - 12,3| = 13-2,4-3| = |1,1| Note:if A,B and C are matrices of the same order, then: 1.A+B= B=B+A (addition of matrices is commutative) 2.A+(B+C)=(A+B)+C(addition of matrices is associative) 3.A+X=B >X =B - A

7.What is the Multiplication of Matrix: Case 1: To multiply a matrix by a scalar, just multiply each of the element of the matrix by the scalar. e.g. |1,2| |3x1, 3x2| |3,6| 3x 13,4| = |3x3 , 3x4| = 19,12||

Case 2: Multiplication of two matrices: Two matrices A and B can be multiplied to each other only if the number of columns in A is equal to the number of rows in B. e.g. |1,2| 14,5| A= 13,4| B= 17,8| let and Number of columns in A = 2 which is equal to the number of rows in B=2. Hence we can multiply these matrices. |1,2| 14,5| |1x4+2x7, 1x5+2x8| |18,21|| AxB = 13,4| x 17,8| 13x4+4x7, 3x5+4x8| = 140,47|