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
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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)