Time allowed: 15 minutes.
1. (2 marks)
Suppose
˜
u
=
⎛
⎝
3
4
2
⎞
⎠
,
˜
v
=
⎛
⎝
2
−
3
3
⎞
⎠
,
˜
w
=
⎛
⎜
⎜
⎝
1
0
0
0
⎞
⎟
⎟
⎠
.
Calculate
˜
u
−
4
˜
v
and 13
˜
u
−
12
˜
v
+
˜
w
if they are defined, or explain why they are not defined.
2. (2 marks)
Find the equation of the line through
⎛
⎝
2
7
−
4
⎞
⎠
and parallel to
⎛
⎝
3
8
1
⎞
⎠
in vector parametric form.
Is the point
⎛
⎝
2
−
1
1
⎞
⎠
on this line? Give a reason for your answer.
3. (3 marks)
Find the intersection of the line
˜
x
=
⎛
⎝
3
0
1
⎞
⎠
+
λ
⎛
⎝
7
−
1
−
1
⎞
⎠
with the plane 3
x
−
2
y
+ 5
z
= 50.
4. (3 marks)
For the following system of equations, write down the corresponding augmented matrix, use Gaussian elimi-
nation to transform the augmented matrix into row-echelon form, and solve the system of equations, writing
your answer in vector form.
x
−
2
y
+ 3
z
=
11
−
x
+ 2
y
+
z
=
−
7
4
x
−
2
y
+ 6
z
=
20
Week 4
Monday 12-1 Class

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