Slide 1 : Subtracting Two Matrices To subtract two matrices, they must have the same order. You simply subtract corresponding entries. Ex.3
Slide 2 : = 5-2 -4-1 3-8 8-3 0-(-1) -7-1 1-(-4) 2-0 0-7 = 2 -5 -5 5 1 -8 5 3 -7 Ex.4
Slide 3 : Multiplying a Matrix by a Scalar In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar.
Slide 4 : -2 6 -3 3 -2(-3) -5 -2(6) -2(-5) -2(3) 6 -6 -12 10 Example:
Slide 5 : Multiplying Two Matrices Let A be m x n and B be n x p matrices. Then the product of matrices A and B denoted by AB is the matrix of order m x p whose (i,j)th element is obtained by adding the products of corresponding elements of i-th row of A and j-th column of B.
i.e.
If the elements in the ith row of A are
ai1 , ai2 , ai3 ,….., ain
and jth column of B are
b1j , b2j , b3j ,….., bnj
Slide 6 : Then (I, j) th element of the product AB is
ai1 b1j + ai2 b2j + ai3 b3j +…+ ain bnj
e.g.
Let A = and B =
Here order of matrix A is 3 ? 3 and that B is 3 ? 4.
? AB is order 3 ? 4. A B
3 ? 3 3 ? 4
Slide 7 : And it is obtained as follows :-
AB = 1.1 + 2.2 + 3.3 1.-1 + 2.4 + 3.2 1.0 + 2.1 + 3.4 1.2 + 2.1 + 3.4 3.1 + 5.2 + 6.3 3.-1 + 5.4 + 6.2 3.0 + 5.3 + 6.3 3.2 + 5.1 + 6.4 1.1 + 1.2 + 3.3 1.-1 + 1.4 + 3.2 1.0 + 1.3 + 3.3 1.2 + 1.1 + 3.4 =
Slide 8 : =
Thus
= 14 13 14 16 31 29 33 35 12 9 12 15 14 13 14 16 31 29 33 35 12 9 12 15
Slide 9 : Exercise :
= 16 -3 14 6 11 -5 40 -6 29 1. 2. 2 7 -8 6 15 -22 10 23 -36 =