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

You’re free to use your calculator’s RREF.

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