Math 22A Section 001
Practice Midterm 02
Name:
Fall Quarter 2014
Student ID Number:
As soon as you read this you must write your Name and Student ID Number at the top of each page.
You will NOT be given extra time to do this at the end of the exam.
There
Math 22A Section 001
Practice Midterm 02 With Solutions
Name:
Fall Quarter 2014
Student ID Number:
As soon as you read this you must write your Name and Student ID Number at the top of each page.
You will NOT be given extra time to do this at the end of t
MAT 22A-001
Practice Midterm 01
Name:
Fall Quarter 2014
Student ID Number:
PLEASE NOTE: On the actual Midterm 01 there are eleven problems worth a total of 100 points. For a perfect exam
score you must do all of these problems correctly. Please dont be c
Name: _._. Student ID Number:
Problem 01(18 points total) On this page. let :1. B. and C' be three :1 x n nonsingular matrices and
let D be an n x n nonsingular diagonal matrix. Using the rules for the inverse and/or transpose of
the product of matrices a
MAT 22A-001
Practice Midterm 01 with Solutions
Name:
Fall Quarter 2014
Student ID Number:
PLEASE NOTE: On the actual Midterm 01 there are eleven problems worth a total of 100 points. For a perfect exam
score you must do all of these problems correctly. P
MAT 22A Section 001
Practice Final Exam
Name:
Fall Quarter 2014
Student ID Number:
As soon as you read this you must write your Name and Student ID Number at the top of each page.
You will NOT be given extra time to do this at the end of the exam.
There
Math 22A Section 001
Midterm 02 With Solutions
Name:
Fall Quarter 2014
Student ID Number:
As soon as you read this you must write your Name and Student ID Number at the top of each page.
You will NOT be given extra time to do this at the end of the exam.
Huy Nguyen
Assignment Strang HW 01 due 01/20/2014 at 12:00pm PST
1. (1 pt) VECTORS
Find the vector from the point (1, 4, 8) to the point
(3, 4, 5).
Enter the coordinates:
MAT22A-Fannjiang-Winter-2014
.
PARAMETRIC EQUATIONS OF LINES
Consider the equation i
MAT 22A Section 001
Practice Final Exam With Solutions
Name:
Fall Quarter 2014
Student ID Number:
As soon as you read this you must write your Name and Student ID Number at the top of each page.
You will NOT be given extra time to do this at the end of th
Huy Nguyen
Assignment Strang HW 8 due 03/14/2014 at 02:00pm PDT
1. (1 pt) What is the matrix P = (Pi j ) for the projection
of a b R3 onto the subspace spanned by the vector
vector
2
a = 7 ?
5
, P1 2 =
, P1 3 =
,
P1 1 =
, P2 2 =
, P2 3 =
,
P2 1 =
P3 1 =
,
Huy Nguyen
Assignment Strang HW 6 due 02/21/2014 at 12:00pm PST
4. (1 pt) How many pivot columns are in this matrix?
3
6 9 96
42
3 3 39
18
A= 3
9 21 36 369 162
.
The number of pivot columns is
1. (1 pt) What is the reduced row echelon form R = rre f (A)
Huy Nguyen
Assignment Strang HW 5 due 02/17/2014 at 12:00pm PST
Is u in N(A)? (Type yes or no.)
Is v in N(A)? (Type yes or no.)
Is w in N(A)? (Type yes or no.)
1. (1 pt) Which of the following sets are subspaces of R3 ?
x
A. y x + y + z = 5
z
x
B.
Huy Nguyen
MAT22A-Fannjiang-Winter-2014
Assignment Strang HW 02 due 01/22/2014 at 12:00pm
PST
The problems appearing on this printout of this problem set are, in general, unique to the student who printed this problem set. In
other words, most of the prob
Huy Nguyen
Assignment Strang HW 4 due 02/05/2014 at 12:00pm PST
-9
-1
3. (1 pt) Given A =
-4
3
4
8. (1 pt) Find the LU factorization of A = -12
-4
.
, use Gauss-Jordon Elimina-
tion to nd
A1 =
.
Given b =
-2
5
MAT22A-Fannjiang-Winter-2014
A =
3
10
7
3
6
Midterm 1
Math 22A, fall 2016
Time: 50 minutes (9 problems, 8 pages)
NAME:
1. Compute the following products and linear combinations. If the operation does not make
mathematical sense, write DNE (Does Not Exist).
[1 point each for parts (a)-(g), 2 points
Homework 8
not to turn in solutions will be posted on Friday Nov 11
1. Suppose that M A = R, with M invertible. We have talked about the relation between
row spaces, column spaces, and nullspaces or A and R. What about the fourth subspace:
what is the pre
Midterm 2
Math 22A, fall 2016
Time: 50 minutes (10 problems, 7 pages, 58 points)
SOLUTIONS
no calculators, books, notes
write answers on the front; feel free to do work on the backs of pages; but if there are
answers on the back please indicate very cle
Homework 8
Solutions
1. Suppose that M A = R, with M invertible. We have talked about the relation between
row spaces, column spaces, and nullspaces or A and R. What about the fourth subspace:
what is the precise relation between N (AT ) and N (RT )?
Firs
Homework 7
Solutions
0 1
0 0
1. Let R =
0 0
0 0
0 0
a) What conditions
1 0 17
b1
0 1 20
b2
0 0 0
, and consider the equation R x = b, with b = b3 .
b4
0 0 0
0 0 0
b5
must the entries of b satisfy in order for R x = b to have a solution?
b3 = 0, b4
Homework 11
Solutions
1. Black and white sheep live in harmony on a pasture. They multiply very quickly! Each
week, for every white sheep, six more white sheep and two black sheep are born; for every
black sheep, three more black sheep and two white sheep
Midterm 1: Solutions
Math 22A, fall 2016
Time: 50 minutes
1. Compute the following products and linear combinations. If the operation does not make
mathematical sense, write DNE (Does Not Exist).
[1 point each for parts (a)-(g), 2 points for (h)]
1
2