Department

MathematicsCourse Code

MATH 33AHProfessor

AllStudy Guide

FinalThis

**preview**shows pages 1-2. to view the full**8 pages of the document.**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:R2→R3is a linear transformation where it is known that T1/2

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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