Math 205b Quiz 02 Worksheet - Linear Algebra, West Bengal State University - 2010
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1Quiz 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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