Determine if the set is a basis for R°. Justify your answer. - 5 -7 -8 - 7 -6 -5 - 3 7 Is the given set a basis for R3? O A. Yes, because these vectors form the columns of an invertible 3x 3 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". O B. Yes, because these vectors form the columns of an invertible 3x 3 matrix. A set that contains more vectors than there are entries is linearly independent. O C. 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. O D. 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".
Determine if the set is a basis for R°. Justify your answer. - 5 -7 -8 - 7 -6 -5 - 3 7 Is the given set a basis for R3? O A. Yes, because these vectors form the columns of an invertible 3x 3 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". O B. Yes, because these vectors form the columns of an invertible 3x 3 matrix. A set that contains more vectors than there are entries is linearly independent. O C. 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. O D. 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".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Determine if the set is a basis for R°. Justify your answer.
1
- 5
- 7
- 7
- 8
- 7
- 6
- 5
- 3
7
Is the given set a basis for R°?
O A. Yes, because these vectors form the columns of an invertible 3×3 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.
C. 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.
D. 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".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11310fdb-10c3-45eb-950b-8d74b6c97def%2Fc3eb326d-4751-41ba-8cd3-871132841559%2Fft0nfmh_processed.png&w=3840&q=75)
Transcribed Image Text:Determine if the set is a basis for R°. Justify your answer.
1
- 5
- 7
- 7
- 8
- 7
- 6
- 5
- 3
7
Is the given set a basis for R°?
O A. Yes, because these vectors form the columns of an invertible 3×3 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.
C. 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.
D. 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".
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