Which of the following sets of vectors are linearly independ

Which of the following sets of vectors are linearly independent? Mark each set which is linearly independent. Hint: You can do this problem without any calculation.

5 1

,

2 8

,

1 3

,

Solution

In order to find whether these are linearly independent or not we need to find the determinant of the given matrices.

Case 1: if the determinant is zero then the vectors are said to be linearly dependent

Case 2: if the determinant is non zero then the vectors are said to be linearly independent

now again the determinant is zero if we have one of the rows and columns as 0

so for given question we have determinant zero for all of these vectors that means all are linearly dependent.