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Final

MATH 33AH Lecture Notes - Lecture 5: Linear Map, Unit Vector, Identity MatrixExam


Department
Mathematics
Course Code
MATH 33AH
Professor
All
Study Guide
Final

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MATH 33A Midterm 1 Jan. 29, 2018
STUDENT NAME:
STUDENT ID NUMBER:
DISCUSSION SECTION NUMBER:
Directions
Answer each question in the space provided. Please write clearly and legibly. Show
all of your work—your work must both justify and clearly identify your final answer.
No books, notes or calculators are allowed. You must simplify results of function
evaluations when it is possible to do so.
For instructor use only
Page Points Score
2 9
3 7
4 6
5 8
6 10
7 10
Total: 50

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Midterm 1, Page 2 of 8 Jan. 29, 2018
1. Suppose T:R2R3is a linear transformation where it is known that T1/2
1/2 =
3
4
2
and T 1/2
1/2=
2
1
1
.
(a) [6 pts] Build the matrix Afor the transformation T.
(b) [3 pts] Find T 2
1.
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Midterm 1, Page 3 of 8 Jan. 29, 2018
2. (a) [5 pts] Write down the three conditions needed for a collection of vectors Vin Rnto be a
subspace. Be precise!
(b) [2 pts] Suppose that T:R11 R345 is a linear function, so that im(T) is a subspace of
R?? and ker(T) is a subspace of R??. Fill in the question marks. Make sure it is clear in
your answer which is which!
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