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Quiz 02 page 1

01/22/2010

Math 205B

Name

Note: On this quiz, use the appropriate notation (e.g. “vector hats”) wherever appropriate. Also, show any rref’s you

use in any problem that requires one.

1. Suppose that A is a 4 × 6 matrix, and consider the matrix equation Ax = b.

1A. How many rows does A have?

1B. How many columns does A have?

h

1C. The vector x belongs to R

for what value of h?

p

1D. The vector b belongs to R

for what value of p?

3 1 1 5

1

3

7

4 2 2 8

1

2

10

2. Suppose that A =

. Let z =

, b =

and d =

.

4 1 3 8

1

1

7

1 2 2 5

0

0

4

Label column vectors of A as a

, a

, a

, and a

.

1

2

3

4

2A. Find the linear combination of a

, a

, a

, and a

represented by Az.

1

2

3

4

2B. Can b be expressed as a linear combination of a

, a

, a

, and a

? Explain why or why not.

1

2

3

4

2C. Find all solutions x of the matrix equation Ax = d.

4

2D. Do the column vectors of A span R

? Explain.

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