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)]#