# Linear combo

pyroknife
Lets say you have 3 vectors v1, v2,v3. They form a 3x3 matrix.

Let's say you're asked if v3 is a linear combo of the other two vectors.

Rref of the matrix gives
1 0 1
0 1 0
0 0 0

The definition of a Linear combo is v3=c1v1+c2v2 where c1 and c2 are scalars.

Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?

Also is 0 a scalar?

Homework Helper
Gold Member
Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?

Also is 0 a scalar?
It IS a linear combination. c2 = 0 is allowed. 0 is a scalar.

Mentor
Lets say you have 3 vectors v1, v2,v3. They form a 3x3 matrix.

Let's say you're asked if v3 is a linear combo of the other two vectors.

Rref of the matrix gives
1 0 1
0 1 0
0 0 0
Assuming this is an augmented matrix, you have c1 = 1 and c2 = 0.
The definition of a Linear combo is v3=c1v1+c2v2 where c1 and c2 are scalars.

Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?
No, v3 is a linear combination of v1 and v2; namely, v3 = 1v1 + 0v2.
Also is 0 a scalar?
Yes, unless you're talking about a 0 vector, which in this case would be <0, 0, 0>.