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Let ⃗u =

[

1

1

]

and ⃗v =

[

−1

0

]

.

1. Graph the vectors ⃗u, ⃗v, and 2⃗u + ⃗v.

2. (a) Draw the set A = {⃗x ∈ R

2

: ⃗x = t⃗u for some t ∈ R}.

(b) Draw the set B = {⃗x ∈ R

2

: ⃗x = t⃗u − (2t + 1)⃗v for some t ∈ R}.

3. (a) Find values of x, y that satisfy the following relationships:

x + y = 7

2x − 3y = 13.

(b) Find values of x, y, z that satisfy the following relationships (your answer may involve

ugly fractions):

x + 2y + 8z = 1

4x + 5y + 8z = 2.

4. Let ⃗w =

[

5

−12]

. Find values of a and b so that

⃗w = a⃗u + b⃗v.

That is, write ⃗w as a linear combination of ⃗u and ⃗v.

5. Let

S = span

1

1

1

,

1

1

0

,

0

0

1

.

Is S a point, line, plane, or all of R

3

? Explain.

1

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