Both sets below are bases for P,: P = {pj, P2, P3} = {1+r?, 1+21, t + 21²} Q = {q,, 42» 93} = {1+3t + 2r², 4 + 5t – 1², – 1 – 41 +1?} (a) Find [1+3t + 2t²| That is, find |91, P (b) Using the same idea from problem (a), "simultaneously" find [1 + 3r + 2r*|, [4 +5t – 1°,, and [-1– 41 +r²],: (c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix PP-0 that such Po-e la + bt +ct*]. = [a + bt + cr*],. P-Q Q (d) Find [9+23t|: (e) Use your matrix from part (c) and matrix-vector multiplication to find 9+ 23t||
Both sets below are bases for P,: P = {pj, P2, P3} = {1+r?, 1+21, t + 21²} Q = {q,, 42» 93} = {1+3t + 2r², 4 + 5t – 1², – 1 – 41 +1?} (a) Find [1+3t + 2t²| That is, find |91, P (b) Using the same idea from problem (a), "simultaneously" find [1 + 3r + 2r*|, [4 +5t – 1°,, and [-1– 41 +r²],: (c) Write the change-of-coordinates matrix from Q to P. That is, find the matrix PP-0 that such Po-e la + bt +ct*]. = [a + bt + cr*],. P-Q Q (d) Find [9+23t|: (e) Use your matrix from part (c) and matrix-vector multiplication to find 9+ 23t||
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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