$30.00
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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