Linear Algebra: Extra Practice Worksheet 4

Here are a few extra Linear Algebra problems. Topics: Image and Kernel of a matrix, subspaces in R^n, and linear independence.

[samibereket]

Thank you for your excellent clarification.

[javierarturorizzosudario.]

Dear Dr. Valerie, for 3b (8:41), I was wondering if it would be okay to use w1, w2, w3, w4, and w5 to find rref first and then pull out all of the redundant vectors, like we did for finding image. I used this way to solve this problem and it seems correct. But I just wanted to make sure it's not by accident :)

[mayrajloredo]

Correct me if wrong, My algebra is rusty but
For x3 shouldn't it be x3=-r-2s?