FOR GMS ICSE 2014 8

Multiplication of Matrics (continued)

I feel that we need to practice multiplication of matrices some more - remember by firend Sir Francis bacon who said "practice maketh perfect !"

So, kindly work our Ex.12 (C) : nos 3, 5, 6 and 7

Remember the steps you need to follow : so let's take sum No.6

• Can we multiply matrix A by matrix B ? Only id the columns in matrix A are equal to the rows of matrix B. A has 3 columns and B has 3 rows. Thus we can multiply matrix A by matrix B. But can we multiply matrix B by matrix A ? Let's see - matrix B has 2 columns and matrix A has 2 rows - so - yes, we can ! Can we multiply matrix A by matrix A ? let's see : matrix A has 3 columns and 2 rows !, so, can we multiply the two matrices ? NO !!!!
• Then we have to see of what order (how many rows and columns) the resultant (after multiplying) matrix is 
• AB will be a 2 x 2 matrix : why ? because it will have the rows of matrix A and the columns of matrix B
• BA will be a 3 x 3 matrix : why ? because it will have the rows of matrix B with the columns of matrix A
• Now taking the first row in matrix AB, let's find
• the left hand side element : = (0 x 0) +  (4 x -1) +  (6 x -5) = 0 + (-4) + (-30) = 0 - 4 - 30 = -34
• the right hand side element : (0 x 1) + (4 x 2) + (6 x -6) = 0 + 8 + (-36) = 0 + 8 -36 = -28
• Now taking the second row in matrix AB, let's find
• the left hand side element : (3 x 0) +  (0 x -1) + (-1 x -5) = 0 + 0 + 5 = 5
• the right hand side element : (3 x 1) + (0 x 2 ) + (-1 x -6) = 3 + 0 + 6 = 9

So, there you are ! All the best ! Day scholars, I look forward to meeting you on the 16th. Boarders, please keep following this blog and working at your maths. Let's hope that you will be able to return on the 18th evening. I'm sure that you're longing to come back ! You must be bored at home !!!!!