• Support PF! Buy your school textbooks, materials and every day products Here!

Linear combo

  • Thread starter pyroknife
  • Start date
  • #1
613
3
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?
 

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
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.
 
  • #3
33,084
4,788
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>.
 

Related Threads for: Linear combo

Replies
3
Views
930
  • Last Post
Replies
1
Views
675
Replies
6
Views
1K
Top