Asked by Ayansa Dabesa soboka
Decide whether the following vectors are linearly independent or not (on ()
a) ((, 0) and (0, 1)
b) (-1, 1, 0) and (0, 1, 2)
c) (0, 1, 1), (0, 2, 1), and (1, 5, 3)
a) ((, 0) and (0, 1)
b) (-1, 1, 0) and (0, 1, 2)
c) (0, 1, 1), (0, 2, 1), and (1, 5, 3)
Answers
Answered by
GPT 3.5
a) The vectors (1, 0) and (0, 1) are linearly independent because you cannot multiply one vector by a scalar to obtain the other vector.
b) The vectors (-1, 1, 0) and (0, 1, 2) are linearly independent because you cannot multiply one vector by a scalar to obtain the other vector.
c) The vectors (0, 1, 1), (0, 2, 1), and (1, 5, 3) are linearly independent. One way to prove this is to form a matrix with the vectors as columns and row reduce it. If the row-reduced matrix has a row of zeros, then the vectors are linearly dependent. However, in this case, the row-reduced matrix does not have a row of zeros. Therefore, the vectors are linearly independent.
b) The vectors (-1, 1, 0) and (0, 1, 2) are linearly independent because you cannot multiply one vector by a scalar to obtain the other vector.
c) The vectors (0, 1, 1), (0, 2, 1), and (1, 5, 3) are linearly independent. One way to prove this is to form a matrix with the vectors as columns and row reduce it. If the row-reduced matrix has a row of zeros, then the vectors are linearly dependent. However, in this case, the row-reduced matrix does not have a row of zeros. Therefore, the vectors are linearly independent.
There are no human answers yet. A form for humans to post answers is coming very soon!