Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) 0-3 9 1 -7 4 - 4 -4 -2 2 OC. If A is the given matrix, then the augmented matrix form of this matrix indicates that Ax = 0 has more than independent set. -1 1 A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax=0 has only the trivial solution. Therefore, the columns of A form a linearly independent set. B. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. represents the equation Ax = 0. The reduced echelon one solution. Therefore, the columns of A form a linearly D. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly independent set.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Determine if the columns of the matrix form a linearly independent set.
Justify your answer.
Select the correct choice below and fill in the answer box within your choice.
(Type an integer or simplified fraction for each matrix element.)
A. If A is the given matrix, then the augmented matrix
form of this matrix indicates that Ax = 0 has only the
independent set.
0 - 3 9
2
1 -7
- 1
4 -4
1
4-2
represents the equation Ax = 0. The reduced echelon
trivial solution. Therefore, the columns of A form a linearly
B. If A is the given matrix, then the augmented matrix
represents the equation Ax = 0. The reduced echelon
form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a
linearly independent set.
C. If A is the given matrix, then the augmented matrix
form of this matrix indicates that Ax = 0 has more than
independent set.
represents the equation Ax = 0. The reduced echelon
one solution. Therefore, the columns of A form a linearly
D. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon
form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a
linearly independent set.
Transcribed Image Text:Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) A. If A is the given matrix, then the augmented matrix form of this matrix indicates that Ax = 0 has only the independent set. 0 - 3 9 2 1 -7 - 1 4 -4 1 4-2 represents the equation Ax = 0. The reduced echelon trivial solution. Therefore, the columns of A form a linearly B. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. C. If A is the given matrix, then the augmented matrix form of this matrix indicates that Ax = 0 has more than independent set. represents the equation Ax = 0. The reduced echelon one solution. Therefore, the columns of A form a linearly D. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly independent set.
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