Math 215 – Intro to Linear Algebra Worksheet #5Coordinate Systems1. Find the vector ~x whose coordinate vector with respect to the basis B =−220,302,4−13is [~x]B=−32−1.2. Find the coordinate vector [~x]Bof ~x =00−2relative to B =113,208,1−13.3. Let B =1−2,−35and let E denote the standard basis for R2.(a) Find the 2 × 2 matrix which transforms B coordinates into E-coordinates.(b) Find the 2 × 2 matrix which transforms E coordinates into B-coordinates.(c) Determine ~x if [~x]B=−13.(d) Determine [~x]Bif ~x =2−5.4. LeteB =1−1,2−1, and recall the basis B given in Problem 3.(a) Find the 2 × 2 matrix which transforms E-coordinates intoeB-co ordinates.(b) Determine [~x]eBfor the vector ~x defined in Problem 3(d).(c) Find the 2 × 2 matrix which tr ansformseB-co ordinates into B-coordinates. Hint: This is a product of twochange-of-coordinate matrices.(d) Verify that the matrix found in (c) transfo rms [~x]eB, found in (b), into [~x]B, found in Problem 3(d).5. Consider the bases B = {1, 1 + x, 1 + x + x2} and E = {1, x, x2} for P2, and let p(x) = 2 − 3x + 5x2.(a) Find the coordinate vector of p(x) with res pect to E.(b) Find the coordinate vector of p(x) with respect to
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