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Problem 1. The figure below shows the vectors u, v, and w, along with the images...

Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure

Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure, and draw onto it the image T(w) as accurately as possible. (Hint: First try writing w as a linear combination of u and v.) TV (u) Problem 2. Let u = | and v Suppose T : R2 + R2 is a linear transformation with 6 1 3) Tu = T(u) = -3 and T(v) = an find T(w). (Hint: See the hint in Problem 1.) 1 -3 Problem 3. Let ej = be the elementary coordinate vectors in R2. Suppose T:R2 → ī 5 [ 3 R3 is a linear transformation with T(ei) = | -3 and T(e2) = | 4 L0 -7 - 3 (a) Find T(w) if w = (b) Give a general formula for T(x). (c) Find a matrix A such that T(x) = Ax for every x € R2.
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2. r-ci+2c2 -. -a +6 =8 = U = 6), 1 = ( ) T: 1R2 IR? TU) = (-), T() = (-3) W = ($) = 666) +(2($) CECI +562) -:- -c,+2c2 =8 =>

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Problem 1. The figure below shows the vectors u, v, and w, along with the images...
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