Dr. Z.s Math 250(1), (Fall 2010, RU) REAL Quiz #7 (Nov. 4, 2010)
NAME: (print!)
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1. (5 points) Find a basis for the following subspace
x
1
x2
4
R : x1 2x2 + 3x3 4x4 = 0
x
Dr. Z.s Math 250(2), (Fall 2010, RU) REAL Quiz #10 (Dec. 9, 2010)
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1. (5 points) Apply the Gram-Schmidt process to replace the given linearly independent set S b
Attendance Quiz for Oct. 4, 2010
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Section:
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1. For the following matrix, A, determine (a) the reduced row echelon form R of A (b) an invertible
matrix P such that
Attendance Quiz for Nov. 4, 2010
NAME: (print!)
Section:
E-MAIL ADDRESS: (print!)
1. A matrix and a vector are given. Show that the vector is an eigenvector of the matrix, and
determine the correspond
Solutions to the Attendance Quiz for Dec. 6, 2010
1. A vector u in R3 and an orthonormal basis S for a subspace W of R3 is given as follows.
2
u= 3 ,
1
1/2
1/ 2
S=
0
1/ 3
1/ 3
1/ 3
,
.
(a) Ob
Solutions to Dr. Z.'s Math 250(2), (Fall 2010, RU) REAL Quiz #6 (Oct. 28, 2010)
1.
Compute the determinant of the following matrix by a cofactor expansion along the second
column.
2
3
3
1 1
4 4
1 45
2
Solutions to Dr. Z.s Math 250(2), (Fall 2010, RU) REAL Quiz #8 (Nov. 11, 2010)
1. (5 points) Determine the dimension of the following subspace. Explain what you are doing!
2s
s + 4t
4
R : s
s
3t
4s
Solutions to the Attendance Quiz for Oct. 11, 2010
1. a) Find an LU decomposition of the following matrix
2 1 1
4 1 4 .
2 1 2
Sol. of 1a): We apply the first phase of Gaussian Elimination bringing it
Attendance Quiz for Oct. 28, 2010
NAME: (print!)
Section:
E-MAIL ADDRESS: (print!)
1. Find a basis for (a) the column space and (b) the null space of the matrix
1
2
0
1
2. Find a basis for the followi
Dr. Z.s Math 250(1), (Fall 2010, RU) REAL Quiz #5 (Oct. 21, 2010)
NAME: (print!)
E-MAIL ADDRESS: (print!)
1. a) Find an LU decomposition of the following matrix
3
4
2
1
1
1
1
4
2
b) Use the answer to
Attendance Quiz for Nov. 29, 2010
Section:
NAME: (print!)
E-MAIL ADDRESS: (print!)
1. Consider the vectors u and v:
1
u = 2
3
,
11
v= 4
1
(a) Prove that u and v are orthogonal to each other.
(b) Co
Answers (and some hints) for the Exam 1 Review Problems
(version of Oct. 13, 2010, 2:15pm, thanks to Devon Peticolas
1. (a) Look it up in the book
(b) No, they are linearly dependent. We have to find
Attendance Quiz for Nov. 11, 2010
NAME: (print!)
Section:
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1. Let v be a non-zero vector in R2 , and let A = vvT (A is a a 2 2 natrix.)
(a) Show that v is an eigenvector of A.
Attendance Quiz for Dec. 13, 2010
NAME: (print!)
Section:
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1. An inconsistent system of linear equations Ax = b is given. Use the method of least squares to
obtain the vectors
Dr. Z.s Math 250(1), (Fall 2010, RU) REAL Quiz #9 (Dec. 2, 2010)
NAME: (print!)
E-MAIL ADDRESS: (print!)
1. (4 points) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal mat
Solutions to Attendance Quiz for Oct. 18, 2010
1.
Compute the determinant of the following matrix along the second row.
2
2
4 0
2
Sol. to 1
:
2
2
det 4 0
2
3
1 1
1 1
2 1
5
1 4 = (0) det
+ ( 1)
1 2
2 2
SOLUTIONS to MATH 250 (1), Dr. Z. ,Exam 1, Thurs., Oct. 14, 2010, 8:40-10:00am,
SEC 202
This Version of Oct. 9, 2016: Thanks for Cassidy Gonzalez [correcting a typo in the
solution of problem 4]
Previ
Attendance Quiz for Sept. 13, 2010
NAME: (print!)
Section:
E-MAIL ADDRESS: (print!)
1. Determine whether the given system is consistent, and if so, find its general solution.
x1 + 3x2 + x3 + x4 = 1
2x
No Title |POLVER05_ |4
128 14
t
T
hnatconv
Uo
Tj
pi
h
cp
rho
Dt
r
A
0.17917
190. 1.
5.
68.
3.141593
1.125 1.0025
60.46
0.5105
0.9210727
55.68805
0.8187312
0.179171
190. 1.
5.
68.
3.141593
1.125 1.0025
No Title |POLVER05_ |4
128 28
t
T
h
rho
cp
N
NPr
Da
NRe
U
0.42918
197.8247
1.125
750. 1.021 1.36 0.54
4.718E+04
393.3421
56.71873
3.608512
0.429181
197.8228
1.125
750. 1.021 1.36 0.54
4.718E+04
393.34
No Title |POLVER05_ |4
128 28
t
T
h
rho
cp
x
kw
k
ho
Dt
u
Z
a
b
N
NPr
Da
NRe
hi
Tj
pi
r
Ao
V
m
Ai
Alm
U
0.04305
72.5 1.125 61.579
1.
0.01042
9.2464
0.3686
1500. 0.979 1.573 0.54 0.6666667
0.3333333
1.
The Second Chance Club for Math 250 (Linear
Algebra), Sections 1-2 Fall 2010 (Rutgers
University)
http:/www.math.rutgers.edu/~zeilberg/LinAlg10/scc.html
.
First Posted: Oct. 19, 2010; Previous Version
Attendance Quiz for Oct. 21, 2010
NAME: (print!)
Section:
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1. Evaluate the determinant of the matrix using elementary row operations.
1
1
3
2
1
4
1
2
8
2. Find the value of c f
Attendance Quiz for Dec. 6, 2010
NAME: (print!)
Section:
E-MAIL ADDRESS: (print!)
1. A vector u in R3 and an orthonormal basis S for a subspace W of R3 is given as follows.
2
u= 3
1
1/2
1/ 2
S=
0
Dr. Z.s Math 250(1), (Fall 2010, RU) REAL Quiz #6 (Oct. 28, 2010)
NAME: (print!)
E-MAIL ADDRESS: (print!)
1. Compute the determinant of the following matrix by a cofactor expansion along the third row
Solutions to Dr. Z.s Math 250(1), (Fall 2010, RU) REAL Quiz #9 (Dec. 2, 2010)
1. (4 points) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix
D such that A = P DP 1
Solutions to Dr. Z.s Math 250(2), (Fall 2010, RU) REAL Quiz #9 (Dec. 2, 2010)
1. (4 points) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix
D such that A = P DP 1