4. Membership in a Span: For every item: (i) apply the Modified Gauss-Jordan Algorithm to determine if b is in Span(S); (ii) write the solution vector if there are solutions to the corresponding augmented matrix; (iii) express b as a linear combination of the vectors in S in the simplest possible way, and check directly that your answer is correct. b = (-4, 2,–3); S = {(7, 4,–6), (-5,–2, 3)} а. b. b = (-4, 2,–4); S = {(7, 4,–6), (-5,–2, 3)} b = (9, 7,–8, 2); S = {(5,-3, 2, 6), (-2,-3, 5, 8), (–5, 4,–2,–3)} с. d. b = (-10, 13,–4, 9); S = {(5,-3, 2, 6), (–5, 4,–2,–3), (-5, 7,–2, 6)} b = (13, 14,–18,-11); {(5,-3, 2, 6), (–2,–3, 5, 8), (–5, 4,–2,–3), (11, 10,–13,–6)} е. S = b = (8,–9,-8, 15,-3), S = {(6,0, 4, 3, 2), (3, 2, 7, 1,–2), (2, 1, 2,–1, 3)} b = (-4,–1, 4, 7,–9), S = {(3, 2, 7, 1,-2), (2, 1, 2, –1, 1), (1, 0,–3,–3, 4)} h. b = (-3, 6,–1,–9,–4), S = {(6,0,–1, 3, 2), (3, 2, –3, 1,–2), (0,–4, 5, 1, 6), (3,–2, 1, 3, 3)} f. g.

4. Membership in a Span: For every item: (i) apply the Modified Gauss-Jordan Algorithm to determine if b is in Span(S); (ii) write the solution vector if there are solutions to the corresponding augmented matrix; (iii) express b as a linear combination of the vectors in S in the simplest possible way, and check directly that your answer is correct. b = (-4, 2,–3); S = {(7, 4,–6), (-5,–2, 3)} а. b. b = (-4, 2,–4); S = {(7, 4,–6), (-5,–2, 3)} b = (9, 7,–8, 2); S = {(5,-3, 2, 6), (-2,-3, 5, 8), (–5, 4,–2,–3)} с. d. b = (-10, 13,–4, 9); S = {(5,-3, 2, 6), (–5, 4,–2,–3), (-5, 7,–2, 6)} b = (13, 14,–18,-11); {(5,-3, 2, 6), (–2,–3, 5, 8), (–5, 4,–2,–3), (11, 10,–13,–6)} е. S = b = (8,–9,-8, 15,-3), S = {(6,0, 4, 3, 2), (3, 2, 7, 1,–2), (2, 1, 2,–1, 3)} b = (-4,–1, 4, 7,–9), S = {(3, 2, 7, 1,-2), (2, 1, 2, –1, 1), (1, 0,–3,–3, 4)} h. b = (-3, 6,–1,–9,–4), S = {(6,0,–1, 3, 2), (3, 2, –3, 1,–2), (0,–4, 5, 1, 6), (3,–2, 1, 3, 3)} f. g.

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

4. Membership in a Span: For every item: (i) apply the Modified Gauss-Jordan Algorithm
to determine if b is in Span(S); (ii) write the solution vector i if there are solutions to the
corresponding augmented matrix; (iii) express b as a linear combination of the vectors in
S in the simplest possible way, and check directly that your answer is correct.
b = (-4, 2,–3); S = {(7,4,–6), (–5,-2, 3)}
а.
b. b = (-4, 2,-4); S = {(7,4,–6), (-5,–2, 3)}
b = (9, 7,-8, 2); S = {(5,-3, 2, 6), (-2,–3, 5, 8), (–5, 4,–2,–3)}
d. b = (-10, 13,–4, 9); S = {(5,-3, 2, 6), (–5, 4,–2,–3), (-5, 7,–2, 6)}
Б - (13, 14, -18, -11)};
S = {(5,-3, 2, 6), (-2,–3, 5, 8), (–5, 4,–2,–3), (11, 10,–13,–6)}
b = (8,-9,-8, 15,–3), S = {(6,0,4, 3, 2), (3, 2, 7, 1,–2), (2, 1, 2, –1, 3)}
Б - (-4,-1,4, 7, -9), S - {{3, 2, 7, 1, -2), (2, 1, 2, -1, 1), (1, 0, -3, -3, 4)}
h. Б - (-3, 6, -1,-9, -4),
S = {(6,0,–1, 3, 2), (3, 2,–3, 1,–2), (0,–4, 5, 1, 6), (3,–2, 1, 3, 3)}
с.
е.
f.
g.

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