UW Common Math 308 Section 4.2.pdf - KEIRAHANSEN...

Current Score : 30 / 30 Due : Thursday, November 9 2017 11:00 PM PST
1. 2/2 points | Previous Answers HoltLinAlg2 4.2.006.
Use the solution method from this example to find a basis for the given subspace.
[3, 0; 5, ­18]
Give the dimension of the basis.
S = span ,
3
5
9
−3
2 2
Solution or Explanation
Row­reduce the matrix with the given vectors as rows,
Thus a basis for S is given by the non­zero row vectors, The dimension is 2.
UW Common Math 308 Section 4.2 (Homework)
KEIRA HANSEN
Math 308, section F, Fall 2017
Instructor: Lucas Braune
WebAssign
The due date for this assignment is past. Your work can be viewed below, but no changes can be made.
Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you
have viewed the answer key. Automatic extensions are not granted if you have viewed the answer key.
Request Extension
~ .
3 5
9 −3
3 5
0 −18
, .
3
5
0
−18

2. 2/2 points | Previous Answers HoltLinAlg2 4.2.010.
Use the solution method from this example to find a basis for the given subspace.
[1, 0; 0, 1; ­1, 2; 1, 0]
Give the dimension of the basis.
S = span , , ,
1
0
−1
1
2
1
0
2
0
1
2
0
3
1
−1
3
2 2

3. 2/2 points | Previous Answers HoltLinAlg2 4.2.014.
Use the solution method from this example to find a basis for the given subspace.
[1, 5; 2, 9; 3, 7]
Give the dimension of the basis.
S = span , ,
1
2
3
5
9
7
−3
−5
−1
2 2
Solution or Explanation
Row­reduce the matrix with the given vectors as columns,
A basis for S is given by column 1 and 2 of the original matrix corresponding to the pivot columns of the row­reduced matrix.
Hence a basis for S is
The dimension is 2.
~ .
1 5 −3
2 9 −5
3 7 −1
1 5 −3
0 1 −1
0 0 0
, .
1
2
3
5
9
7

4. 2/2 points | Previous Answers HoltLinAlg2 4.2.015.
Use the solution method from this example to find a basis for the given subspace.
[1, 3; ­1, ­5; 0, 10; 2, 8]
Give the dimension of the basis.
2 2