Determine if the columns of the matrix form a linearly independent set. 1 3 -3 6 3 10 -7 12 28 0-6 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 the set contains more vectors, than there are entries in each vector, (Type whole numbers.) B. 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 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.
Determine if the columns of the matrix form a linearly independent set. 1 3 -3 6 3 10 -7 12 28 0-6 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 the set contains more vectors, than there are entries in each vector, (Type whole numbers.) B. 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 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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 26EQ
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Transcribed Image Text:Determine if the columns of the matrix form a linearly independent set.
1 3-3 6
3 10 -7 12
28 0-6
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 the set contains more vectors,
, than there are entries in each vector,
(Type whole numbers.)
O B. 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 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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