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Midterm

Exam2210Sample4Exam


Department
Mathematics
Course Code
MATH 2211
Professor
All
Study Guide
Midterm

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MT T  S 
I S. Y
M , 
Q . THE MATRIX OF A LINEAR TRANSFORMATION
Define the linear transformation T:R3ÏR3so that
x1
x2
x3
x1+x2+x3
x1x2+x3
x1x2x3
.
a.) Find the standard matrix of T.
b.) Is Tone-to-one? Explain.
c.) Is Tonto? Explain.
d.) If there is any, find a vector v such that T(v) =
bwhere
b=
2
2
1
.
1

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Q . MATRIX OPERATIONS
Define the linear transformations T:R3ÏR3and S:R3ÏR3so that
T
x1
x2
x3
=
2x12x2+x3
3x2x3
x3
and S
x1
x2
x3
=
2x12x2+x3
x23x3
x3
.
a.) Find the standard matrix of ST.
b.) Find the standard matrix of TS.
c.) Find, if there is any, a vector v such that (ST)(v) =
bwhere
b=
1
1
0
.
2
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