Question

In any vector space R which of the following is TRUE?

Options:

The set which contain only single non-zero vector is linearly independent

The set which contain only zero vector is linearly independent

Every superset of a linearly independent set is linearly independent

Every subset of a linearly dependent set is linearly dependent

Answer 1

Answer:

3..is the option not answer but 2nd is correct

Answer 2

The statement which is True is: Every superset of a linearly independent set is linearly independent.

Explanation for the answer:

• Let us take an example.
• We have three vectors, (1,1), (1,2), and (2,3) which are linearly dependent.
• As the third is the sum of the other two, the first two are linearly independent.
• Hence, subsets of linearly independent sets are linearly independent.
• Hence, the Statement which is True is: Every superset of a linearly independent set is linearly independent.

(#SPJ2)