Math 2010 Homework #7 Name_________________________________ You’re free to use your calculator’s RREF. For #1 – #5, let ? = [ – 2 4 1 -2 3 – 6 ], and de

Math 2010 Homework #7 Name_________________________________
You’re free to use your calculator’s RREF.

For #1 – #5, let ? = [
– 2 4

1 -2
3 – 6

], and define ?: R2 ? R3, by ?(?) = ??. Then T is a linear transformation

(I promise).

1. Find ? ([
– 1

5
]). See an example.

2. Find all x (if any) such that ?(?) = [
22

-11
-33

]. Write your answer in parametric vector form. See an

example.

Math 2010 Homework #7 Name_________________________________
You’re free to use your calculator’s RREF.

3. Find all x (if any) such that ?(?) = [
23

-11
-33

]. Write your answer in parametric vector form.

Based on your answers to #2 and #3 above, you now know that T is neither one-to-one nor onto.

4. Explain how you now know that T is not one-to-one.

5. Explain how you now know that T is not onto.

Math 2010 Homework #7 Name_________________________________
You’re free to use your calculator’s RREF.

For #6 – #11, simply use RREF along with the pivot column/row test to tell me if the linear

transformation defined by ?(?) = ?? is one-to-one and/or onto. No work need be shown on these, just

circle “one-to-one” if it’s one-to-one and/or circle “onto” if it’s onto (leave blank if it’s neither). See an

example.

6. ? = [
1 3 4
2 4 3

] One-to-one Onto

7. ? = [
1 3 4
2 6 8

] One-to-one Onto

8. ? = [
1 3
2 6
5 15

] One-to-one Onto

9. ? = [
1 3
2 6
5 16

] One-to-one Onto

10. ? = [
1 3 1
2 6 0
5 15 1

] One-to-one Onto

11. ? = [
1 2 1
2 6 0
5 15 1

] One-to-one Onto

Math 2010 Homework #7 Name_________________________________
You’re free to use your calculator’s RREF.