Determine if the columns of the matrix form a linearly independent set. 1 2 -3 6 3 7 -6 3 8 -1 -6 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. The columns of the matrix do not form a linearly independent set because there are more entries in each vector, than there are vectors in the set, (Type whole numbers.) O B. The columns of the matrix do not form a linearly independent set because the set contains more vectors, (Type whole numbers.) than there are entries in each vector, O C. Let A be the given matrix. Then the columns of the matrix form a linearly independent set since the vector equation, Ax = 0, has only the trivial solution. D. The columns of the matrix form a linearly independent set because at least one vector in the set is a constant multiple of another.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Determine if the columns of the matrix form a linearly independent set.
1 2
- 3
6.
3 7
- 6
9.
3 8 - 1
- 6
...
Select the correct choice below and, if necessary, fill in the answer box(es) within
your
choice.
O A. The columns of the matrix do not form a linearly independent set because there are more entries in each vector,
than there are vectors in the set,
(Type whole numbers.)
B. The columns of the matrix do not form a linearly independent set because the set contains more vectors,
than there are entries in each vector,
(Type whole numbers.)
C. Let A be the given matrix. Then the columns of the matrix form a linearly independent set since the vector equation, Ax = 0, has only the trivial solution.
O D. The columns of the matrix form a linearly independent set because at least one vector in the set is a constant multiple of another.
Transcribed Image Text:Determine if the columns of the matrix form a linearly independent set. 1 2 - 3 6. 3 7 - 6 9. 3 8 - 1 - 6 ... Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. The columns of the matrix do not form a linearly independent set because there are more entries in each vector, than there are vectors in the set, (Type whole numbers.) B. The columns of the matrix do not form a linearly independent set because the set contains more vectors, than there are entries in each vector, (Type whole numbers.) C. Let A be the given matrix. Then the columns of the matrix form a linearly independent set since the vector equation, Ax = 0, has only the trivial solution. O D. The columns of the matrix form a linearly independent set because at least one vector in the set is a constant multiple of another.
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