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Consider the ordered basis B = {(1, −1,0), (1, 1, 1), (0, 1, 1)} of R³. Give the coordinate vector v = (-3, -4,-3) with respect to B: CB(V) =

Consider the ordered basis B = {(1, −1,0), (1, 1, 1), (0, 1, 1)} of R³. Give the coordinate vector v = (-3, -4,-3) with respect to B: CB(V) =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 22EQ
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Consider the ordered basis B = {(1, −1,0), (1, 1, 1), (0, 1, 1)} of R³. Give the coordinate vector v = (-3,-4, -3) with respect to B: CB(v) = Let T: R³ → P3 be given as T((1,0,0)) = 5x* + (3)x2+(2)x+(6), T((0, 1,0)) = 2x³ + (3)x² + (2)x+ (0), and T((0, 0, 1)) = −7x³ + (1)x² + (−6)x + (1). Then T(v) = Compute T((1,-1,0)) : = T((1, 1, 1)) = T((0, 1, 1)) = x³+ x3+ x³ + x²+ x²+ x²+ x+ x+ x+ x+ Let D= {x3, x3+x corresponding to the ordered basis B and D: MDBT) = + x + 1} be an ordered basis of P3. Compute the matrix of T
Transcribed Image Text:Consider the ordered basis B = {(1, −1,0), (1, 1, 1), (0, 1, 1)} of R³. Give the coordinate vector v = (-3,-4, -3) with respect to B: CB(v) = Let T: R³ → P3 be given as T((1,0,0)) = 5x* + (3)x2+(2)x+(6), T((0, 1,0)) = 2x³ + (3)x² + (2)x+ (0), and T((0, 0, 1)) = −7x³ + (1)x² + (−6)x + (1). Then T(v) = Compute T((1,-1,0)) : = T((1, 1, 1)) = T((0, 1, 1)) = x³+ x3+ x³ + x²+ x²+ x²+ x+ x+ x+ x+ Let D= {x3, x3+x corresponding to the ordered basis B and D: MDBT) = + x + 1} be an ordered basis of P3. Compute the matrix of T
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