Q32 of 124 Page 186

If prove that for all n ∈ N.

Given :


Matrix A is of order 2 2.


To prove :


Proof :


A =


Let us assume that the result holds for An – 1


An – 1 =


We need to prove that the result holds for An by mathematical induction .


An = An – 1 × A = =


An = =


An =


More from this chapter

All 124 →
30

Find the values of a and b for which


 31

If find f(A), where f(x) = x2 – 5x + 7.

 33

Given an example of two matrices A and B such that

A ≠ O, B ≠ O, AB = O and BA ≠ O.


 34

Give an example of three matrices A, B, C such that

AB = AC but B ≠ C.