Quiz study guide

Week 11 (Wed, March 30) Third Quiz study guide

Lecture videos 8a, 8b, 9a, 9b, 10a, 10b
Lecture video 11a, only definition of kernel and image, and computation like in Exercise 2 and 3. Subspaces won’t be on this quiz.
Wk07 wksheet (based on lectures 8a, 8b)
Wk10 wksheet (based on lectures 9a, 9b, 10a)
Wk11 wksheet (the first six problems only)
Additional Gradescope practice with solutions, taken from reading hw 8a, 8b, 9a, 9b
Additional Gradescope practice with solutions, taken from reading hw 10a, 10b
Key definitions:
- definition of eigenvalue, eigenvector
- saying that a function preserves addition is the same as saying …
- saying that a function preserves scalar multiplication is the same as saying …
- definition of the standard basis vectors
- definition of the kernel of a matrix
- definition of the image of a matrix
Key computation and/or proof to practice:
- Given a number lambda, find all eigenvectors of lambda (if any) using row reduce
- Given a matrix A and corresponding linear transformation, determine its domain and its taget
- Showing that a function preserves addition
- Showing that a function does not preserve addition
- Showing that a function preserves scalar multiplication
- Showing that a function does not preserve scalar multiplication
- Given a formula of a linear transformation T, find the matrix A for T (via the algorithm using standard basis vectors)
- Given a vector v and a matrix A, determine whether v is in the kernel of A
- Given a vector v and a matrix A, determine whether v is in the image of A

Note:

The quiz will be at the beginning of class. Scratch paper will be provided.
Know your ID number, since you will need to write it on the quiz paper.
Calculators are not permitted and are not needed (no simplification is needed).

Past quizzes

Study guide for previous quizzes