Math 281
Homework
Nov. 16th
1. Which of the following functions f : R → R are linear functions?
(a) f (x) = x
(b) f (x) = x + 2
(c) f (x) = 2x
(d) f (x) = x2
R2
2. Let f :
3
f(
)?
3
2
→ R be a linear function such that f (
) = 4. What is
2
2
) = 4 and
3. Let f :
→ R be a linear function such that f (
2
1
6
f(
) = 5. What is f (
)?
0
4
3
2
4. Can you have a linear function f : R → R such that f (
)=4
0
1
) = 5? Why?
and f (
0
4
2
2
2
and
)=
5. Let f : R → R be a linear function such that f (
1
1
8
3
1
)? Can you tell me what is the
. What is f (
f(
)=
2
3
0
image of f ?
R2
6. Let f : R2 → R2 be a linear function, and v1 , v2 two vectors that
are
not proportional to each
other. Assume you know that f (v1 ) =
a11
a12
and f (v2 ) =
. What is f (αv1 + βv2 )? Can you express
a21
a22
this result in terms of matrix multiplication?
1