2 9 Theorem Let F V U And G U W Be Linear Transformations Fix Bases B C E In V U W Respectively Then Go 1 (23.99 KiB) Viewed 70 times
: 2.9. Theorem. Let f: V + U and g: U + W be linear transformations. Fix bases B, C, E in V,U, W respectively. Then [go f] = [ 91.1 i.e. the matric of the composition gof is the product of the matrices of g and f in the fixed bases. BE CE BC
Problem 4 (2 points): Let f: Pi + P2 be defined by p(x) + xp(2). Let g: P2 + P2 be defined by P(1) + p'(x). Let B = {1, 2} be the canonical basis in P1 and C = {1, 2,2%}be the canonical basis in P2. Compute (gºf) in two ways: (a) by finding gof directly and then computing its matrix; (b) by finding the matrices of f, g and using Theorem 2.9 in Notes (page 49). B+C
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