Answer to Question #40089 in Linear Algebra for saba

Question #40089

Can all vector in vector space be linearly independent?

Expert's answer

No, it is impossible. Since, av also lies in vector space if v lies in the vector space, a is a scalar. Nevertheless, vector av is not linearly independent, it is linearly dependent on v.

Learn more about our help with Assignments: Linear Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Is it is possible for vector spaces to have no linearly independent vector?
2. Investigate the nature of the conic 5x2+4xy+2y2+2x+y=1.
3. Find the normal cononial form of the quadratic form 2xy+2yz-x2-y2-z2. Hence compute its signature.
4. Obtain an orthogonal basis with respect to the standard inner product for the subspace for R4 define
5. Find the dual basis of the basis e1=(1,1,2) , e2=(1,0,1) , e3=(2,1,0) of the vector R3 over R.
6. Let a quadratic form has expression 6x2+5xy+10y2 with respect to the standard basis of R2. Find its
7. Find the rank of the quadratic form 2x2+2y2+3z2-xy+4yz+5xz.