Will rate if all questions answer 1. +-1 points WWCMDiffEaLinAlg1 5.6.002c. Let

Question

Will rate if all questions answer

1. +-1 points WWCMDiffEaLinAlg1 5.6.002c. Let W denote the linear span of the given set of vectors. Select from the vectors a basis for W. (Enter your answers as a comma-separated list.) v1 = (1,-1.1,-1), v2 = (9,-1, 7, 1). v3 = (-4,-4,-2,-6), v.-(18,-2, 14, 2 Additional Materials eBook 2. -1 points WWCMDiffEQLinAIg1 5.6.002a Let W denote the linear span of the given set of vectors. Select from the vectors a basis for W. (Enter your answers as a comma-separated list v1-(0, 6, 3), v2 . (1, ?, 1), ?. (-1, 1, 1) Additional Materials eBook

Explanation / Answer

1)

Here v4 = 2*v2

This implies that {v4, v2} are linearly dependent.

And the set {v1, v2, v3} is linearly independent and spans W.

Hence the set {v1, v2, v3} forms a basis for W.

2)

av1 +bv2 + cv3 =0

(b-c, 6a+3b+c, 3a+b+c) =(0,0,0)

This implies that

b-c =0, 6a+3b+c =0 and 3a+b+c=0

b=c

6a+4b=0

3a+2b=0

Take b=1 be arbitrary

Then c=1 and a =-2/3

This implies that the set {v1,v2, v3} is linearly dependent.

And v1 = (3/2)v2 + (3/2) v3

i.e v1 is a linear combination of v2, v3.

Hence the set {v2,v3} is linearly independent and it spans W.

Hence {v2, v3} forms a basis for W.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.