Determine if the set is a basis for R³. Justify your answer. 3 6 -5 3 2 11 0 3 Is the given set a basis for R³? O A. Yes, because these vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". B. Yes, because these vectors form the columns of an invertible 3x3 matrix. A set that contains more vectors than there are entries is linearly independent. OC. No, because these vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". D. No, because these vectors do not form the columns of a 3x3 matrix. A set that contains more vectors than there are entries is linearly dependent.
Determine if the set is a basis for R³. Justify your answer. 3 6 -5 3 2 11 0 3 Is the given set a basis for R³? O A. Yes, because these vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". B. Yes, because these vectors form the columns of an invertible 3x3 matrix. A set that contains more vectors than there are entries is linearly independent. OC. No, because these vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". D. No, because these vectors do not form the columns of a 3x3 matrix. A set that contains more vectors than there are entries is linearly dependent.
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
![Determine if the set is a basis for R³. Justify your answer.
][₁
3
3
11
0
3
Is the given set a basis for R³?
OA. Yes, because these vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theorem, the following
statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span
R".
B. Yes, because these vectors form the columns of an invertible 3x3 matrix. A set that contains more vectors than there are entries
is linearly independent.
O C. No, because these vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following
statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span
R".
D. No, because these vectors do not form the columns of a 3x3 matrix. A set that contains more vectors than there are entries is
linearly dependent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F799db758-6264-477e-875f-1cfecc426da7%2Fbcb0c497-dda6-4591-8b11-d8a7f2575c8f%2Fvyaz65l_processed.png&w=3840&q=75)
Transcribed Image Text:Determine if the set is a basis for R³. Justify your answer.
][₁
3
3
11
0
3
Is the given set a basis for R³?
OA. Yes, because these vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theorem, the following
statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span
R".
B. Yes, because these vectors form the columns of an invertible 3x3 matrix. A set that contains more vectors than there are entries
is linearly independent.
O C. No, because these vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following
statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span
R".
D. No, because these vectors do not form the columns of a 3x3 matrix. A set that contains more vectors than there are entries is
linearly dependent.
Expert Solution
Step 1
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 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,
