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FP1 Matrices Question

Review Exercise #2, Question 20 if you have the book.

A, B and C are 2 x 2 matrices.

a) Given that AB = AC, and that A is not singular, prove that B = C.
b) Given that AB = AC, where A = (3,6,1,2) and B = (1,5,0,1), find a matrix C whose elements are all non-zero.

Done part a, but I'm stuck on part b :frown:

Help please! :biggrin:
ohh i remember when matrices used to be in FP3...ahh the days
a) pre multiply both sides by a^-1
b) I suspect it may be a brute force C = (a b )(c d) job
Reply 3
Avatar for Zhen Lin
Zhen Lin
12
Find a suitable matrix H such that AH = 0, then C = B + H works. You can find such a H in much the same way you find eigenvectors of A - in particular, we want H to be a matrix with columns the eigenvectors corresponding to a zero eigenvalue.
Reply 4
Avatar for RBarack
RBarack
2
You could have just posted the whole question ..
Reply 5
Avatar for implus
implus
OP
2
^ That is the whole question.

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