Math 205a,b - Linear Algebra Matrix Worksheet With Answer Key
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1MATH 205A,B - LINEAR ALGEBRA
FALL 2015
QUIZ 3
NAME:
Section:(Circle one)
A(8 : 00)
B(9 : 30)
Show ALL your work CAREFULLY.
Let
1
3
3
5
A =
.
1
7
(a) Solve the homogeneous equation Ax = 0.
The corresponding augmented matrix
1
3 0
1
3 0
1
3 0
1
3 0
1
3 0
1 0 0
3
5
0
3
5
0
0
14
0
0
1
0
0
1
0
0 1 0
.
1
7
0
0
4
0
0
4
0
0
4
0
0
0
0
0 0 0
The solution is x
= 0 = x
.
1
2
(b) Based on your answer to (a), determine whether the columns of A are linearly independent?
Justify your answer.
Since Ax = 0 has only the trivial solution, the zero vector can only be the trivial linear
combination of the columns of A. Hence the columns of A are linearly independent.
3
(c) Do the columns of A span
? Explain.
No. Since there are only two vectors (columns), the span of two vectors can be at
2
3
most
so the columns of A do not span
.
0
0
Alternatively, the equation Ax =
0
has no solution (CHECK!) so the vector
0
1
1
does not lie in the span of the columns of A.
Date: September 28, 2015.
1
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