Q26 of 28 Page 3

If and I is the identity matrix of order 2, show that

We know that I

Now, LHS = I + A


=


And on RHS = (I – A)






As we know,

cos 2θ = 1 - 2 sin2 θ

cos θ =  2 cos2 θ - 1

and sin2θ = 2 sinθ cosθ



As tanθ = sinθ/cosθ



=


= LHS


Hence Proved.

More from this chapter

All 28 →
24

Find the inverse of each of the following matrices by using elementary row transformations:

 25

A trust invested some money in two types of bonds. The first bond pays 10% interest and the second bond pays 12%. The trust received Rs 2800 as interest. However, if trust had interchanged money in bonds, they would have got Rs 100 less as interest. Using matrix method, find the amount invested by the trust.

 27

Find A, if .

 28

Find x, y, z if satisfies A’ = A–1