Scribd
Upload
70 views1 page

Math 114: Homework 6

The set of vectors is linearly independent. A vector that is not a linear combination of the given vectors is (1, 0, 0). Zero can be expressed as a nontrivial linear combination of the vectors. The set of matrices B is a basis for M2×2. The set of polynomials B is a basis for P3[t].

Uploaded by

Jerico Arciaga
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
70 views1 page

Math 114: Homework 6

The set of vectors is linearly independent. A vector that is not a linear combination of the given vectors is (1, 0, 0). Zero can be expressed as a nontrivial linear combination of the vectors. The set of matrices B is a basis for M2×2. The set of polynomials B is a basis for P3[t].

Uploaded by

Jerico Arciaga
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

Math 114: Homework 6

1 2 1



2 4 2
1. Determine if the set , , is linearly independent. Justify your answer.

2 5 1




3 1 9

2. Write DEP if the set of vectors is linearly dependent, otherwise, write IND.

4
1 2
1
1 2

(a) 0 , 1 , 3 Ans: (c) 2 , 1 , 2 Ans:


0 0 3 3 1 2

(" # " # " #)
0 1 1 8 1 1
(d) , , Ans:




0 2 1 2 6 1
(b) , ,
0 3 1 Ans:





0 4 1

3 6 1
3. Let v1 = 1 , v2 = 2 , v3 = 2 .

2 4 5

(a) Find b R3 that is not a linear combination of v1 , v2 , v3 .


(b) Express 0 as a nontrivial linear combination of v1 , v2 , v3 .
(" # " # " # " #)
1 0 1 0 0 1 0 1
4. Is B = , , , a basis for M22 ?
0 1 0 1 1 0 1 0

5. Determine if B = {5 3t + 4t2 + 2t3 , 9 + t + 8t2 6t3 , 6 2t + 5t2 , |{z}


t3 } is a basis for P3 [t].
| {z } | {z } | {z }
v1 (t) v2 (t) v3 (t) v4 (t)

You might also like