Let T : R2 → P2 be a linear transformation, and let B= {u1 = [1 2] , u2 = [2 5] }be a basis for R2. if T(u1) = 2x+1 and T(u2) = x^2 +1, find T([a b]) in terms of a and b.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let T : R2 → P2 be a linear transformation, and let B= {u1 = [1 2] , u2 = [2 5] }be a basis for R2. if T(u1) = 2x+1 and T(u2) = x^2 +1, find T([a b]) in terms of a and b. [Hint: First express b as a coordinate vector in the basis B.]

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