Solve a linear system to determine whether the given vectors u, v, and w are linearly independent or dependent. If they are linearly dependent, find scalars a, b, and c not all zero

such that au + bv + cw=0.

5

-340-3

v=

1 W= -4

u=

8

1

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

O A. The vectors u, v, and w are linearly independent.

O B.

The vectors u, v, and w are linearly dependent, where a =

(Simplify your answers.)

b=

and c = 1, where the value of c is chosen to be equal to 1.

Ç 282692 Dc

Create Order | Last: On

okay.

that w/nFind |a-b|, 2a + b, and 4a - 5b.

- 3

1

0-8

1 b= -4

4

3

a=

|a-b|= √30

(Simplify your answer. Type an exact answer, using radicals as needed.)

2a + b =

(Simplify your answer. Type your answer in the form ai + bj + ck.)/nShow that the given set V is closed under addition and multiplication by scalars and is therefore a subspace of R³.

X

V is the set of all y such that y = 0.

X

u

Let a = 0 and b= 0 be two vectors in V. Find their sum a + b.

a+b=

Z

x+u

Z

Z+W

W

0 (Simplify your answer.)

The vector sum a + b is not an element of the set V because it does not have its second component equal to

(Type an integer or a f

is not

is

q3

Reference

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Subject Lin

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Comment

Therefore, V is closed under addition.