a) Let Vbe a vector space with basis B = {b₁, b₂}. Let T: R² → R² be a linear transofrmation so that Find matrix [T]B to T with care to the basis B. 1 2 T (b₁) = b₁ – 5b2, T (b₂) = −3b₁ + 9b2. b) Let C1 = 2b₁ + b2, C₂ = b₁ + b₂. explain why C = {C₁, C2} is a basis for V. What is the transition matrix PBC from basis C to basis B? c) Find matrix[T]c to T with care to basis C.

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A: The answer is given below:

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A: Solution is below.

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A: see my solutiuon

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