Posted by **Ashley** on Sunday, May 20, 2007 at 4:45pm.

If v1,...,v4 are in R^4 and v3 is not a linear combination of v1, v2, v4 then {v1, v2, v3, v4] is linearly independent.

Is this true or false? Why?

If v1,...,v4 are in R^4 and v3 is not a linear combination of v1, v2, v4 then {v1, v2, v3, v4] is linearly independent.

This is equivalent to the statement:

If {v1, v2, v3, v4} is

**NOT** linearly independent then v3

**IS** a linear combination of v1, v2, v4 .

This is false. If {v1, v2, v3, v4} is linearly dependent, then that means that there exists real numbers a1, a2, a3 and a4, not all equal to zero such that:

a1 v1 + a2 v2 + a3 v3 + a4 v4 = 0

Now, if a3 is not zero, then you can write v3 as a linear combination of the other three vectors, but this need not be the case.

## Answer This Question

## Related Questions

- math - If A^TA is an invertible matrix, prove that the column vectors of A are ...
- Discrete Math - True or False? Homogeneous linear recurrence equations are ...
- Chemistry - 1. A combination reaction may also be a displacement reaction. True ...
- Chemistry: Answer check please! - 1. Reactions follow the law of conservation of...
- Linear algebra - Find two vectors v and w such that the three vectors u = (1,-1...
- linear algebra- check question - I just want to make sure my reasoning is ...
- 7th grade health true or false - 11. Disagreements are a normal part of life. (1...
- Science - 1. Scientists are not concerned with the human impact on the ...
- Physical Ed - 11. Disagreements are a normal part of life. (1 point) True False ...
- CHECK ANSWERS AND HELP PLEASE - if P(A)=.60, P(A/B)=.50, AND P(B)= .40, answer ...

More Related Questions