Question

Find a basis and determine the dimension for each of the following subspaces: (a) W= \{ [2s - t, s, t, s] | s and t are any real numbers \} (b) All the vectors [x, y, z] in $R^3$ such that x - y + 2z = 0 (in other words, y = x + 2z) (c) Span of the set of vectors \{ (0, 3, -2), (4, 0, 3), (-8, 15, -16) \}

          Find a basis and determine the dimension for each of the following subspaces:
(a) W= \{ [2s - t, s, t, s] | s and t are any real numbers \}
(b) All the vectors [x, y, z] in $R^3$ such that x - y + 2z = 0 (in other words, y = x + 2z)
(c) Span of the set of vectors \{ (0, 3, -2), (4, 0, 3), (-8, 15, -16) \}

$Find a basis and determine the dimension for each of the following subspaces: (a) W= { [2s - t, s, t, s] | s and t are any real numbers } (b) All the vectors [x, y, z] in R^3 such that x - y + 2z = 0 (in other words, y = x + 2z) (c) Span of the set of vectors { (0, 3, -2), (4, 0, 3), (-8, 15, -16) }$

Added by Michelle M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/02/2023

Step 1

This shows that W is the span of the vectors {[2, 1, 0, 1], [-1, 0, 1, 0]}. To find a basis, we can check if the vectors are linearly independent. Show more…

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Find a basis and determine the dimension for each of the following subspaces: a) W = {[2s - t, s, t, s] | s and r are any real numbers} b) All the vectors [xyz] in R such that x^2z = 0, in other words y = 2z c) Span of the set of vectors {0, 3, 24, 38, 151}