If B is the standard basis of the space P3 of polynomials, then let B={1, t, t², t³}. Use %3D coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. (1– t)³, (2 – t)?, 3 – 1t- 21² + t³

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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If B is the standard basis of the space P3 of polynomials, then let B= {1, t, t, t°}. Use
%3D
coordinate vectors to test the linear independence of the set of polynomials below. Explain
your work.
(1 – t)3, (2 – t)², 3 – 1t- 2? + 13
...
Write the coordinate vector for the polynomial (1 - t)°, denoted p,.
P1
Transcribed Image Text:If B is the standard basis of the space P3 of polynomials, then let B= {1, t, t, t°}. Use %3D coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. (1 – t)3, (2 – t)², 3 – 1t- 2? + 13 ... Write the coordinate vector for the polynomial (1 - t)°, denoted p,. P1
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