Determine if the columns of the matrix form a linearly independent set. 1 3-3 9 27-3 6 3 12 2-17 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, than there are entries in each vector, (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 9 27-3 6 3 12 2-17 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, than there are entries in each vector, (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.
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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![### Determining Linear Independence of Matrix Columns
#### Problem Statement
Evaluate whether the columns of the matrix form a linearly independent set.
\[
\begin{bmatrix}
1 & -3 & 3 & 9 \\
2 & 7 & -3 & 6 \\
3 & 12 & 2 & -17
\end{bmatrix}
\]
---
#### Choices
Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
1. **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.)
2. **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.)
3. **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.
4. **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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8109dbb5-39b2-442d-b17d-793e299fca4a%2F4f34b7ab-5184-41f4-92dd-859e7c3cfca9%2Fbtlkbas_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining Linear Independence of Matrix Columns
#### Problem Statement
Evaluate whether the columns of the matrix form a linearly independent set.
\[
\begin{bmatrix}
1 & -3 & 3 & 9 \\
2 & 7 & -3 & 6 \\
3 & 12 & 2 & -17
\end{bmatrix}
\]
---
#### Choices
Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
1. **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.)
2. **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.)
3. **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.
4. **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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