How to do questions b?

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1 Answer
Feb 4, 2018

bb(Y)=[(-11/16,17/16),(-1/4,3/4)]

Explanation:

First find bb(A^-1)

The easiest way to find the inverse of bb(A) is to find the determinant of bb(A):

This is just:

(3xx6)-(1xx2)=16

Next switch the elements on the leading diagonal of bb(A) and change the signs of the elements on the non-leading diagonal of bb(A)

So you should have:

[(6,-2),(-1,3)]

Divide each element by the determinant bb(16):

[(6/16,-2/16),(-1/16,3/16)]=[(3/8,-1/8),(-1/16,3/16)]

bb(A^-1)=[(3/8,-1/8),(-1/16,3/16)]

Now:

bb(YA)+bb(B)=bb(C)

bb(YA)=bb(C-B)

Using bb(A^-1)

bb(YA A^-1)=bb((C-B)A^-1)

bb(Y)=bb((C-B)A^-1)

Note we are post multiplying on both sides. This is important as Matrix multiplication is non-commutative.

i.e.

bb(AB)!=bb(BA) ( In general )

bb(C-B)=[(3,4),(2,6)]-[(4,-1),(2,2)]=[(-1,5),(0,4)]

:.

bb(Y)=[(-1,5),(0,4)][(3/8,-1/8),(-1/16,3/16)]=[(-11/16,17/16),(-1/4,3/4)]

bb(Y)=[(-11/16,17/16),(-1/4,3/4)]