### Assignment Instructions/ Description

Image transcription textDetermine if the vectors are linearly independent. Justify your answer.

CO

6

0

4

12

O

8

- 48

The vector equation has

so the vectors

V

linearly independent.... Show moreImage transcription textDetermine if the columns of the matrix form a linearly independent set. Justify your answer.

1 - 5

3 3

-5 25 - 15 3

. . .

Choose the correct answer below.

O A. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector.

O B. The columns of the matrix do not form a linearly independent set because there are more entries in each vector than there are vectors in the set.

O C. The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector.

O D. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set.... Show moreImage transcription textDetermine whether the statement below is true or false. Justify the answer.

If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S.

Choose the correct answer below.

A. The statement is true. If S is linearly dependent then for each j, vi, a vector in S, is a linear combination of the preceding vectors in S.

B. The statement is true. If an indexed set of vectors, S, is linearly dependent, then at least one of the vectors can be written as a linear combination of other vectors in the set. Using the basic properties of equality, each of the vectors in the linear

combination can also be written as a linear combination of those vectors.

O C. The statement is false. If an indexed set of vectors, S, is linearly dependent, then it is only necessary that one of the vectors is a linear combination of the other vectors in the set.

O D. The statement is false. If S is linearly dependent then there is at least one vector that is not a linear combination of the other vectors, but the others may be linear combinations of each other.... Show moreImage transcription text3

2

5

- 6

2 - 4

Given A =

-3 -2 -5

observe that the third column is the sum of the first and second columns. Find a nontrivial solution of Ax = 0 without performing row operations. [Hint: Write Ax = 0 as a vector equation.]

4

0

4

1.7.37

. . .

X =... Show moreImage transcription textDetermine if v is in the set spanned by the columns of B.

2

- 3

2

- 8

6

- 6

8

- 6

B=

V=

6

-3 13

12

6

0 21

30

. . .

Choose the correct answer below and, if necessary, fill in the answer box(es) to complete your choice.

O A. Vector v is in the set spanned by the columns of B because

by +

b 2 +

b3 = V.

O B. Vector v is in the set spanned by the columns of B because the columns of B span R4.

O C. Vector v is not in the set spanned by the columns of B because the reduced echelon form of the matrix formed by writing B with a fourth column equal to v is

O D. Vector v is not in the set spanned by the columns of B because the columns of B, b1, b2, and by are linearly independent.... Show moreï¿½