Determine if the columns of the matrix form a linearly independent set. Justify your answer. [1 -2 5 2; -2 4 -10 2; 0 1 -1 3] Choose the correct answer below. 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. B. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. C. 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. D. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector.
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Step 1: Identify the matrix given in the question: The matrix given in the question is: \[ \begin{bmatrix} 1 & -2 & -5 & 2 \\ -2 & -24 & -10 & 3 \\ Show more…
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Determine if the columns of the matrix form a linearly independent set. Justify your answer. [ 1 -4 4 3] [-4 16 -16 3] Choose the correct answer below. A. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector. 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. C. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. D. 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.
Zhumagali S.
Determine if the columns of the matrix form a linearly independent set. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. 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. 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.
Manisha S.
Use determinants to decide if the set of vectors is linearly independent. The determinant of the matrix whose columns are the given vectors is . (Simplify your answer.) Is the set of vectors linearly independent? A. The set of vectors is linearly dependent, because the determinant is not zero. B. The set of vectors is linearly independent, because the determinant exists. C. The set of vectors is linearly independent, because the determinant is not zero. D. The set of vectors is linearly dependent, because the determinant exists.
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