FOR GMS ICSE 2014 22nd Aug

Ex.Today, we need to draw our attention to :

Ex.12 (C) Nos. 4, 16, 18, 21, 29 and Ex.12 (D) : Nos 1, 2, 3, 7, 9, 10, 14, 17, 18

In all these sums we are trying to find the value of unknown elements : x, y, a, b, c and so forth.

Various mathematical operations have been used : addition, subtraction, multiplication and division.

Points to remember :

• a NULL or ZERO matrix is a matrix in which all elements in the matrix are 0
• an IDENTITY is a matrix is a SQUARE matrix in which all the elements excelpt the elements in the primary diagonal are 0
• In multiplication first note the order of each matrix before you need to multiply and note the order of the resultant matrix
• If you are doing the following matrix A - 2B, multiply the matrix B by 2 (i.e. each element of the matrix will be multiplied by 2) and then subtract the result from matrix A. Do not multiply each element in matrix B by -2 !

Ex.12 (C) : 17, 25,  Ex.12 (D) : 4, 6

In these sums you need to find the value of an unknown Matrix M

Points to remember :

• e.g.in Ex.12 (C) 17 (i) : 
• First we need to ask : in what order will the matrix M be if when it is multiplied with a matrix with an order 2 x 2, results in a matrix with an order 1 x 2 ? The answer is that the order of matrix M will be 1 x 2 - why ? because the resultant matrix [1  2] takes the row of the first matrix and the columns of the second matrix.
• Since M is a matrix of the order 1 x 2, then we can let it be [x   y] 
• now you proceed in multiplying matrix M and the 2 x  matrix
• then proceed to find the values of x and y as you did in the sums above.

Ex.12 (C) : 30, Ex.12 (D) : 5, 20

In these sums we find that we need to fill in the trignometircal values for certain numbers.

Before doing the sums we need to revise the values of sin, cos and tan for 0, 30, 45, 60 and 90 degrees. then you carry on !

You have quite a few sums to do today ! However, in the three types of sums, there's just a slight change in the type. The main work is practice - especially when multiplying matrices. One needs to be careful !

Remember, if you have any difficulty, I am only an e-mail away !