Midterm
1
Math 20F
Lin
Winter
2010
Place all books, calculators, and papers under your desk , On the cover of your blue book write your name,
student ID number, section time, and color of your exam, You may have a 3 x 5" card of handwritten notes, In a
column number one to five on the front of your blue book, Show all your work, and box your answers, You must
give Correct reasons for each answer to obtain full credit.
(a) 10 pts, Find
AI
(b) 5 pts, Write
b
as a linear combination of the columns of
A.
(Your answer should only involve numbers,)
2,
(a) 6 pts, Find the matrix of the linear transformation
T
:
1R2
+
1R2 that first reflects points through the
vertical
X2
axis and then rotates points counterclockwise
¥
radians,
(b) 3 pts, Is
T
one to one?
1
4
4.
(a) 8 pts, Express
C)
as two different linear combinations of
(~3)
,
(:8)
,
(;3)
,
_
T
.
(1
2)
_
(0
1)
_
(1
(b) 3 pts,
Compute
BA

C
If
A

3
4
.
B
1
0
' C 
0
5,
The following statements are either true or false.
If
the statement is true, prove it.
If