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Quiz

Quiz8Spr11mt210AnsExam


Department
Mathematics
Course Code
MATH 2211
Professor
All
Study Guide
Quiz

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MT Q 
İ S. Y
M , 
Surname, Name:
Q . §. S  Rn
Let Abe the 4×5matrix
5 2 0 88
4 1 2 89
5 1 3 5 19
85 6 8 5
.
A) Find the null space of A.
B) Find the column space of A.
C) Find a basis for the null space of A.
D) Find a basis for the column space of A.
A .
Before we answer the parts in the question, we need to reduce the given
matrix. We see that
5 2 0 88
4 1 2 89
5 1 3 5 19
85 6 8 5
1 0 0 60 122
010154 309
001 47 94
0 0 0 0 0
.
(A) We need to solve Ax= 0. Note that x1, x2, x3are basic, x4and x5are free
variables. Therefore, we see that
Nul A =
x4
60
154
47
1
0
+x5
122
309
94
0
1
:x4, x5R
which is a subspace of R5.
(B) Col A is the set of all linear combinations of the columns of A. Therefore,
we see that
Col A =
c1
5
4
5
8
+c2
2
1
1
5
+c3
0
2
3
6
+c4
8
8
5
8
+c5
8
9
19
5
:x4, x5R
1
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