Math Problem Statement

Determine if the columns of the matrix form a linearly independent set. Justify your answer. left bracket Start 4 By 3 Matrix 1st Row 1st Column 0 2nd Column negative 8 3rd Column 16 2nd Row 1st Column 3 2nd Column 1 3rd Column negative 14 3rd Row 1st Column negative 1 2nd Column 5 3rd Column negative 4 4st Row 1st Column 1 2nd Column negative 5 3rd Column negative 2 EndMatrix right bracket 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    enter your response here represents the equation Axequals0. The reduced echelon form of this matrix indicates that Axequals0 has more than one solution.​ Therefore, the columns of A form a linearly independent set. B. If A is the given​ matrix, then the augmented matrix    enter your response here represents the equation Axequals0. The reduced echelon form of this matrix indicates that Axequals0 has more than one solution.​ Therefore, the columns of A do not form a linearly independent set. C. If A is the given​ matrix, then the augmented matrix    enter your response here represents the equation Axequals0. The reduced echelon form of this matrix indicates that Axequals0 has only the trivial solution.​ Therefore, the columns of A do not form a linearly independent set. D. If A is the given​ matrix, then the augmented matrix    enter your response here represents the equation Axequals0. The reduced echelon form of this matrix indicates that Axequals0 has only the trivial solution.​ Therefore, the columns of A form a linearly independent set.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Theory
Linear Independence
Row Reduction

Formulas

Ax = 0 (homogeneous system)
Reduced Row Echelon Form (RREF)

Theorems

Linear Independence Theorem
Row Echelon Form and Pivot Theorem

Suitable Grade Level

College Level (Linear Algebra)