# linear algebra

Feb 3rd, 2012
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Consider two bases B = b1, b2 and C = c1, c2 for a vector space V such that b1 = c1 - 2c2 and b2 = 3c1 - 4c2. Find the change-of-coordinates matrix from B to C.

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(1)Determine which of the following sets is a subspace of Pn for an appropriate value of n.(A)Consider is the subspace of , since Consider Let is a constant and in space (B)Is not spaceFor example:Consider , does not have degree 3.(C)Is not spaceFor example:Consider are have positive coefficients and the degree at most 3, but has the negative coefficient.Therefore, answer is (2)Determine vector space.A vector space ( or linear space ) consists of the following :A field of scalars.A set of objects, called vectors.A rule ( or operation ) called vector addition, which associates with each pair of vectors in a vector in , called the sum of , in such a way that.Addition is commutative Addition is associative There is a unique vector in called the zero vector such that for all in For each vector in there is a unique vector in such that A rule called scalar multipli

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