Math 308E
Midterm Exam 2
Page 1 of 5
Name:
Problem
Points
1
16
2
10
3
8
4
8
Total
Score
42
Instructions
You may use a scientic calculator and one sheet (two-sided) of handwritten notes. Other notes,
books, electronic devices, and graphing calculators are
Math 308E
Midterm Exam
Page 1 of 5
Name:
Problem
Points
1
8
2
8
3
8
4
10
Total
Score
34
Instructions
You may use a scientic calculator and one sheet (two-sided) of handwritten notes. Other notes,
books, electronic devices, and graphing calculators are no
Math 308 Homework 1 selected solutions
#38, Section 1.1.
Solution. We will use row operations to remove the x1 from one of the equations. First, write
the system as an augmented matrix:
a11 a12 b1
a21 a22 b2
.
Gaussian elimination proceeds dierently depen
Math 308E
Midterm Exam 2
Page 1 of 5
Name:
Problem
Points
1
16
2
10
3
8
4
8
Total
Score
42
Instructions
You may use a scientic calculator and one sheet (two-sided) of handwritten notes. Other notes,
books, electronic devices, and graphing calculators are
Math 308 Homework 6
Due Friday, February 28.
Textbook problems:
3.4: 13, 23, 32, 33
3.5: 17, 23, 26, 27, 30, 40 (hint: to show N (AB) = N (B), you should show that if v is
in N (AB), then v is in N (B), and conversely that if v is in N (B) then v is in
Math 308 Writing Assignment 1 Solution
1. Suppose that A is an m n matrix whose columns are a1 , . . . , an , and that x is a column
vector in Rn :
x1
.
x = . .
.
xn
Show that Ax is the vector x1 a1 + + xn an .
Solution. Since the columns of A are a1
Math 308 Writing Assignment 2
Due Friday, February 28.
1. Say V and W are two subspaces of Rn . The intersection of V and W , denoted V W , is
the set of vectors which are in both V and W . Show that V W is a subspace of Rn .
1
Math 308 Homework 7
Due Friday, March 14.
Textbook problems:
3.8: 7, 11
4.1: 1, 15, 17
4.4: 9 (ignore the part about algebraic multiplicity)
4.7: 3, 6
4.8: 1, 3, 7, 9
Also do the following extra problem:
1. (a) Some linear transformations respect geo
Math 308 Writing Assignment 1
Due Friday, January 24.
1. Suppose that A is an m n matrix whose columns are a1 , . . . , an , and that x is a column
vector in Rn :
x1
.
x = . .
.
xn
Show that Ax is the vector x1 a1 + + xn an .
2
1 2 3
(As an example,
Math 308 Homework 4
Due Wednesday, February 12.
Textbook problems:
1.9: 1, 11, 18, 48, 74
3.1: 13
3.2: 1, 5, 6, 8, 18, 19
Other problems:
1. Heres one application of vectors in high-dimensional space, which also provides a review of
dot products and ve
Math 308 Homework 3
Due Wednesday, January 29.
Textbook problems:
1.5: 56, 66
1.6: 1, 26
1.7: 1, 2, 9, 15, 40
Other problems:
1. Suppose A is a 2 3 matrix, and B is a 3 5 matrix:
A=
a11 a12 a13
,
a21 a22 a23
b11 b12 b13 b14 b15
B = b21 b22 b23 b24 b25
Math 308 Homework 5
Due Wednesday, February 19.
Textbook problems:
3.3: 5, 16, 18*, 22, 26, 30, 44, 52*.
3.4: 1, 3, 9
* The algebraic specication you give should be an equation/system of equations dening
the subspace S, e.g. S is the line x + 2y 3z = 1,
Math 308 Homework 1
Due Wednesday, January 15.
Textbook problems:
1.1: 7, 15, 26, 30, 38.
1.2: 2, 5, 23, 24, 45
Also do the following extra problem. (Note: This is not one of the writing assignment
problems, though you should still think about writing a
Math 308E
Midterm Exam
Page 1 of 5
Name:
Problem
Points
1
8
2
8
3
8
4
10
Total
Score
34
Instructions
You may use a scientic calculator and one sheet (two-sided) of handwritten notes. Other notes,
books, electronic devices, and graphing calculators are no