Ok, I've got 3 questions.
1) Given C and D are square matrices of order n, and inverse of C ( ) exists, expand and simplify as much as possible.
My answer turns out to be
Is this the most you can simplify it? And is the way I stated alright? Or should I do it like
2) Let u be any unit vector in , and let uu (where the T indicates that the matrix is transposed).
I can do a) but I cannot do b). Can anyone help me?
a) For B a square matrix, expand the product (I + B)(I − B + B^2)
b) Let = , and find and
c) Using the matrix B and the result from part (b), simplify the formula in (a).
d) Let = = for B in b).
Use the results in (c) and (a) to find .
Note: represents the identity matrix. Also recall that if , if and only if ,
Ok, for this question I can do all the way up to c but then I am lost how to do d). I mean I can do it by row reducing A and then finding the inverse that way. But the question says to use my results from a and c so I am thinking there must be abother way to do it. Can anyone help me out here?
My result for a) turns out to be I + B^3. Subsequently I find that B^3 is a 3x3 matrix with all zeros and thus my answer in c turns out to be just "I", the identity matrix.
Thanks in advance for all your help!