Q18 of 28 Page 3

If , prove that .

We will be proving the above equation by putting different values of n (i.e. n = 1, 2, 3 ….n)

For n=1,



For n=2,


A2 = A.A



For n=3,


A3 = A2.A




r n=4,


A4 = A3.A




d so on for other values of n.


If we notice each result, then we will see that it is of same type that we are trying to prove.


So we can generalise the above results for all n ϵ N


Hence Proved

More from this chapter

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16

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways; telephone, house calls and letters. The cost per contact (in paise) is given matrix A as


The number of contacts of each type made in two cities X and Y is given in matrix B as



Find the total amount spent by the group in the two cities X and Y.

 17

If then prove by principle of mathematical induction that for all n ∈ N.

 19

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below:


(a) If unit sale prices of x, y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively, find the total revenue in each market with the help of matrix algebra.


(b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise respectively. Find the gross profit.

 20

If then show that A is a root of the polynomial f(x) = x3 – 6x2 + 7x + 2.