If anyone you help with the last part of c i'd be very grateful!
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LHS
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- 30-03-2011 21:52
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- 30-03-2011 22:19
What does the first part of (c) tell you about the span
<B^n, B^(n-1), ... , B^2, B, I>?
(PS the Oxford mods papers are online and may be easier to link to directly rather than producing a scan)Last edited by RichE; 30-03-2011 at 22:20. -
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- 30-03-2011 22:23
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- 30-03-2011 22:48
Hmm.. I must be being rather slow, still not really getting it. The first part of c tells us that the span <B^n, B^(n-1), ... , B^2, B, I> can equal zero for certain values of a[i] not equal to zero, so B^i are dependent? Don't know if that's helpful. Not sure about rewriting the span using the identity from the first bit, sorry!
Oh wait, if B^i are linearly Dependant then they span the 3x3 matrices so there exists a linear combination that creates the required matrix?Last edited by LHS; 30-03-2011 at 22:52. -
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- 31-03-2011 10:16
If
, then what can be said about the set
, with regards to linear independence/dependence?
Also, note that we cannot havebeing a linearly independent set for
(irrespective of what B actually is), since the dimension of the space of 3 x 3 matrices is 9, and a linearly independent set cannot have more elements than the dimension of the space it is in.
So getting back to the question - it's possible to write the LHS of the equation at the end of C entirely in terms of B and I, can you see why?Last edited by Mark13; 31-03-2011 at 10:21.
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