Determine if the columns of the matrix form a linearly independent set. Justify
ID: 3034698 • Letter: D
Question
Determine if the columns of the matrix form a linearly independent set. Justify your answer. [-2 -1 0 0 -1 6 1 1 -12 2 1 -24] Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent set. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A form a linearly independent set If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly independent set.Explanation / Answer
The RREF of the given matrix is
1
0
0
0
1
0
0
0
1
0
0
0
Therefore, the columns of A are linearly indepredent.
Option C is the correct answer. If A is the given matrix, then the augmented matrix
-2
-1
0
0
0
-1
6
0
1
1
-12
0
2
-1
-24
0
represents the equation Ax = 0.The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A form a linearly independent set. If the equation Ax = 0 has only the trivial solution , then A can be row reduced to the identity matrix. Hence the columns of A are linearly independent. Here, the given system has 4 linear equations in 3 variables, one of which is redundant.
1
0
0
0
1
0
0
0
1
0
0
0
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