3) Let C be a basis that contains vectors2 2 -2 4-244-2(1 + (−1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 + (−1) x + 2x² + 2x³), (1 + 2x + (−1) x² + (−1) x³), P =1 1 1 4-12 4 4and [x] B=-8-=Then :X =

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Answered: 3) Let C be a basis that contains…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Are the following vectors a basis of R²?
x-3x+1 7. Is the set {(1,2,-1,3), (1, -1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an- swer.
Find the coordinates of x = {-10, 2, 4} with respect to the basis consisting of u, {1, 3, 2}, u, = {2, 1, 4}, and u; = {1,0, 6}. -
a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x) = -3x² + 2x – 5 , and q(x) = -x+5x? b) Verify that the basis set S = {(3,0,4), (-4,0,3), (0,1,0)} is orthogonal then find the coordinates of the vector u = (-5,5,1) using inner product
Express each of the following vectors in R² as linear combinations of the vectors [4] and (a) (b) (c) (d) 16 11 -36 17 -12 15 -20 = || = || - 4 Y + Y + -4 + Y + + + + A 4 -
3) Find a basis of F3 containing the vectors (1, 2, -3), (2, 6, -3)
Say you are given two vectors x and y represented using different basis sets {ê;} and {f;}, of the same dimension N. That is, x = y = E y;f;. E xie; and N you are told that a given vector x has the representation x = (1, 1)" in basis {ê;} and the representation x = (-1,1)" in basis {f}}. How might the two basis sets be related? Draw a figure to justify X = your answer.
b
Suppose V is a subspace of R" and suppose {v1, v2, v3} is a basis of V. Decide if the following sets of vectors are a basis for V: (i) {v2, v1 – 503, 2v3} (ii) {v2, v1 – 503, 203, 302 + 703 – v1} (iii) {202 – v3, v1}

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3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 + (-1) x + 2 and [x] B = Then : X = 1