Question

Determine if the vectors are linearly independent. v1 = [ 4, -1 ], v2 = [ -8, 2 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The vectors are not linearly independent because if c1 = [ ] and c2 = 1, both not zero, then c1v1 + c2v2 = 0. B. The vectors are linearly independent because the vector equation x1v1 + x2v2 = 0 has only the trivial solution.

          Determine if the vectors are linearly independent.
v1 = [ 4, -1 ], v2 = [ -8, 2 ]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The vectors are not linearly independent because if c1 = [ ] and c2 = 1, both not zero, then c1v1 + c2v2 = 0.
B. The vectors are linearly independent because the vector equation x1v1 + x2v2 = 0 has only the trivial solution.

Determine if the vectors are linearly independent.
v1 = [ 4, -1 ], v2 = [ -8, 2 ]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The vectors are not linearly independent because if c1 = [ ] and c2 = 1, both not zero, then c1v1 + c2v2 = 0.
B. The vectors are linearly independent because the vector equation x1v1 + x2v2 = 0 has only the trivial solution.

Added by Pilar G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Avinash Vishwakarma

04/28/2022

Step 1

Vectors are linearly independent if the only solution to the equation c1V1 + c2V2 + ... + cnVn = 0 is the trivial solution, where all coefficients c1, c2, ..., cn are zero. If there exists a non-trivial solution (where at least one coefficient is not zero), the Show more…

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Determine if the vectors are linearly independent. v1 = [4, -1], v2 = [-8, 2] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The vectors are not linearly independent because if c1 = [ ] and c2 = 1, both not zero, then c1v1 + c2v2 = 0. B. The vectors are linearly independent because the vector equation x1v1 + x2v2 = 0 has only the trivial solution.