Let W = span{(1, 1, 0), (1, 0, 1), (2, 1, 1), (0, 1, -1)}. i. Is (9,0,9) in W? Justify your answer. ii. Is W = R³? Justify your answer.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 15E
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a) ] Let W = span{(1, 1,0), (1,0, 1), (2, 1, 1), (0, 1, – 1)}.
i. Is (9,0,9) in W? Justify your answer.
ii. Is W = R³? Justify your answer.
1 2
3]
1
3
3
1
b) Let A =
1
Lo
1
2
i. Find the reduced row echelon form of A.
ii. Find a basis for the subspace spanned by the rows ofA.
iii. Find a basis for the subspace spanned by the columns of A.
Transcribed Image Text:a) ] Let W = span{(1, 1,0), (1,0, 1), (2, 1, 1), (0, 1, – 1)}. i. Is (9,0,9) in W? Justify your answer. ii. Is W = R³? Justify your answer. 1 2 3] 1 3 3 1 b) Let A = 1 Lo 1 2 i. Find the reduced row echelon form of A. ii. Find a basis for the subspace spanned by the rows ofA. iii. Find a basis for the subspace spanned by the columns of A.
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