M260 LINEAR ALGEBRA

EXAM1 (Chapters 1 and 2)

Name:_____________________________

Time: 75 minutes

No books, no notes, no calculators.

Show all work on these pages.

Use arrow notation for vectors.

1 Let T be the counter-clockwise rotation about the origin in of 45 degrees.

a. Find the matrix A of T.

b. Find T.

2. .

a.

b.

b. Solve the equation

3. Find a polynomial whose graph goes through the points (0,1), (1,0), (-1,0), (2,-15). Then sketch the graph.

4. Consider the vector

a. First, draw the lines and the vector on the same coordinate system.

b.

c. Last, check that your answer is correct and show your check.

5.

6. Which of the following linear transformations are invertible? (i.e. have inverses). Describe the inverses of those which are invertible; explain why those that are not invertible are not invertible.

a. Projection onto a line.

Not invertible since any 2 vectors along a line of projection will have the same output (i.e. not 1-1).

b. .

c. .

7.