Suppose a1, a2, a3, a4, and a, are vectors in R°, A = (a1 | a2 a3 a4 a5), and 0 0 0 1 0 [1 -5 5 rref(A) 4 2 0 1 1 -3 a. Select all of the true statements (there may be more than one correct answer). A. span{a1, a2} = R³ B. {a1, a2} is a linearly independent set |C. {a1, a2, a3, a4} is a basis for R3 D. span{a1, a2, a3} = R³ E. span{a1, a2, a3, a4} = R³ F. {a1, a2, a3} is a linearly independent set G. {a1, a2, a3, a4} is a linearly independent set |H. {a1, a2} is a basis for R3 O1. {a1, a2, a3} is a basis for R3 b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE. a4 = c. The dimension of the column space of A is and the column space of A is a subspace of d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { } e. The dimension of the null space of A is and the null space of A is a subspace of f. If x1 = (5, –4, –1,1,0), then Ax1 Is x1 in the null space of A? choose v g. If x2 = (-5, -2, 3,0, 1), then Ax2 = . Is x2 in the null space of A? choose h. If x3 3x2 – 4x1 : then Ax3 . Is x3 in the null space of A? choose i. Find a basis for the null space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as a comma separated list of vectors. A basis for the null space of A is { }
Suppose a1, a2, a3, a4, and a, are vectors in R°, A = (a1 | a2 a3 a4 a5), and 0 0 0 1 0 [1 -5 5 rref(A) 4 2 0 1 1 -3 a. Select all of the true statements (there may be more than one correct answer). A. span{a1, a2} = R³ B. {a1, a2} is a linearly independent set |C. {a1, a2, a3, a4} is a basis for R3 D. span{a1, a2, a3} = R³ E. span{a1, a2, a3, a4} = R³ F. {a1, a2, a3} is a linearly independent set G. {a1, a2, a3, a4} is a linearly independent set |H. {a1, a2} is a basis for R3 O1. {a1, a2, a3} is a basis for R3 b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE. a4 = c. The dimension of the column space of A is and the column space of A is a subspace of d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { } e. The dimension of the null space of A is and the null space of A is a subspace of f. If x1 = (5, –4, –1,1,0), then Ax1 Is x1 in the null space of A? choose v g. If x2 = (-5, -2, 3,0, 1), then Ax2 = . Is x2 in the null space of A? choose h. If x3 3x2 – 4x1 : then Ax3 . Is x3 in the null space of A? choose i. Find a basis for the null space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as a comma separated list of vectors. A basis for the null space of A is { }
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Suppose a1, a2, a3, a4, and a, are vectors in R°, A = (a1 | a2 a3 a4 a5), and
0 0
0 1 0
[1
-5
5
rref(A)
4
2
0 1
1
-3
a. Select all of the true statements (there may be more than one correct answer).
A. span{a1, a2} = R³
B. {a1, a2} is a linearly independent set
|C. {a1, a2, a3, a4} is a basis for R3
D. span{a1, a2, a3} = R³
E. span{a1, a2, a3, a4} = R³
F. {a1, a2, a3} is a linearly independent set
G. {a1, a2, a3, a4} is a linearly independent set
|H. {a1, a2} is a basis for R3
O1. {a1, a2, a3} is a basis for R3
b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE.
a4 =
c. The dimension of the column space of A is
and the column space of A is a subspace of
d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or
<1,2,3,4,5>. Enter your answer as a comma separated list of vectors.
A basis for the column space of A is {
}
e. The dimension of the null space of A is
and the null space of A is a subspace of
f. If x1 = (5, –4, –1,1,0), then Ax1
Is x1 in the null space of A? choose v
g. If x2 = (-5, -2, 3,0, 1), then Ax2 =
. Is x2 in the null space of A? choose
h. If x3
3x2 – 4x1 :
then Ax3
. Is x3 in the null space of A? choose
i. Find a basis for the null space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or
<1,2,3,4>. Enter your answer as a comma separated list of vectors.
A basis for the null space of A is {
}
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
