Math 2660-125
Exam 4
10/27/2011
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Each problem counts 5 points.
1. (1) What is the rank of a matrix (denition)?
1
2
2
3
2
5
4
8
(2) Find the rank of the matrix A =
1 3 2 5
0
2
0
4
.
Solution.
(1) The rank of a matrix is the dimension of its ro
Math 2660-125
Exam 3
10/13/2011
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Each problem counts 5 points.
1. Determine whether the set
x1
S = x2 : x1 + x2 = x2 R3
3
x3
is a subspace of R3 . Explain your answer.
Recall that a nonempty subset S of a vector space V is a subspace of V if S
Math 2660-125
Exam 2
09/22/2011
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Each problem counts 5 points.
101
1. Let A = 3 3 7 .
213
(a) Find A1 and verify your answer.
(b) Use A1 to solve Ax = b for b = (1, 2, 3) .
Solution.
(a) Applying elementary row operations on [A|I ] to get reduc
Math 2660-125
Exam 1
09/08/2011
PRINT Name:
Each problem counts 5 points.
1. Solve the following system of linear equations, applying elementary row operations on
the augmented matrix to get strict upper triangular form rst and then applying back
substitu