Thursday

August 21, 2014

August 21, 2014

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

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

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.

**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: 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...

7th grade health true or false - 11. Disagreements are a normal part of life. (1...

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 ...

Reading - can you help me thank you: 2.Detecting bias is one of the major keys ...

English - 1.) Anyone can publish information on the Internet without fact-...

Statistics - When comparing two samples that are independent of one another, we ...