hints

[hybrid lodge]

How to do it?

[sleek wolf]

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   +close
   

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[stable minnow]

Suppose you have linearly independent x1, x2, ..., xn. A new set of vectors made out of their linear combinations can be represented as AX, where A is a n⨯n matrix and X is a column vector {x1, x2, ..., xn}^T.
Then the resulting set is also linearly independent if |A| ≠ 0. So, write the matrix and check whether its determinant is 0.

[hybrid lodge]

Yeah here linearly addition?

[stable minnow]

What?

[hybrid lodge]

Here the options are different

And they are saying row operations

[hybrid lodge]

When we add or substract A b discarded

They can not give determinant non zero

[hybrid lodge]

I am confused how to discard C and D?

[hybrid lodge]

@stable minnow

Sry for ping

[stable minnow]

As I said above, find the determinants of the respective matrices. May be better to bring them to the REF first.

[hybrid lodge]

Here all are known varibles

I only know that if I add two independent vectors then it will surely form linearly dependent vectors

And same for substraction