Mathematics 33A, First Midterm, October 16, 2009.
Calculators, books, or notes of any kind are not allowed on this exam. Do not use any paper
other than that provided. (You may write on the back if you need more space, but indicate
this clearly on the front.)
There are 11 items on this exam altogether, and they all have equal value. Answer as many
of them as you can.
The questions are not always arranged in order of difficulty.
Look
through them when you start so you get an idea of the time you’ll need. If you’re not sure
what to do on an item then move onward and return to it later. (Some of the questions can
be solved with geometric reasoning instead of lengthy computations; this may save you some
time.)
Good luck.
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Question 1.
Solve the system of equations
braceleftbigg
3
x
+ 2
y

z
+ 2
w
=
3
3
x
+ 6
y

z
=
5
.
Question 2.
Compute the product

1
0
0
1
1
2
·
parenleftbigg
0
1
2
1
2
3
parenrightbigg
.
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 Spring '08
 lee
 Math, Linear Algebra, orthogonal projection

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