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

- Linear Algebra - Let v1 = (1, 0, ?1) v2 = (0, 2, 2) v3 = (?3, 4, 7) and let W = ...
- 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 ...
- Linear Algebra - p1, p2, p3 are elements of P_2 p1(x)= 1+x-2*x^2 p2(x)= 2+3x-x^2...
- Linear algebra - Find two vectors v and w such that the three vectors u = (1,-1...
- Chemistry: Answer check please! - 1. Reactions follow the law of conservation of...
- linear algebra- check question - I just want to make sure my reasoning is ...
- linear algebra - Solve using the concept of rank. Is S={−16 −7 &#...
- 7th grade health true or false - 11. Disagreements are a normal part of life. (1...

More Related Questions