# PP - PRACTICE PROBLEMS Here are some practice problems...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PRACTICE PROBLEMS Here are some practice problems. Their range of difficulty is considerable. They were thrown together fairly quickly; if you think you see a mistake, let us know. You should not read anything significant into the distribution of questions. For example, there are a lot of diagonalizability questions below. That does not mean that there are a lot diagonalizability questions on the exam. It means that we like syllables. Determine if 1 2 3 4 , 2- 1 2 1 , 1 2 3- 1 , 2- 1 2 4 is linearly independent. A linear transformation T : V → W , where V is the set of 3 × 3 matrices and W = R 4 , has a 6-dimensional null space. Let A be the standard matrix of T . What is the dimension of (Nul A ) ⊥ ? Let T : R 2 → R 2 rotate vectors clockwise by π , and then reflect them in the line x + y = 0. Find the standard matrix for T . Let r ∈ R n be fixed. Prove that T : R n → R n , given by T : x 7→ proj r x , is a linear transformation. Is it injective? Surjective?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

PP - PRACTICE PROBLEMS Here are some practice problems...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online