Answer to Question #219747 in Linear Algebra for aia

Question #219747

Let V and W be vector spaces over F, where V is n-dimensional. Let K ≤ V and R ≤ W

be finite-dimensional subspaces such that dim K + dim R = n. Prove that there exists a linear transformation L : V → W such that ker L = K and Im L = R.

Expert's answer

Answer in progress...

Learn more about our help with Assignments: Linear Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. What do you mean by Norm of an Inner Product Space
2. Find the nature of the matrix of QF is x2 +y2 +z2-2xy-2yz-2zx.
3. find a linear transformation T:R^3->R^3 whose image is spanned by (1,2,3 ) and (4,5,6)
4. . let t:r^2->r^2 be a linear transformation for which ( 1,2)= (2,3 ) and ( 0,1)= (1,4 ). find a f
5. find basis and dimension of the subspace W of V spanned by A = [[1 2] [-1 3]], B = [[2 5] [1 -1]], C
6. a. Find the orthogonal and normal canonical forms of 2y^2-2yz+2zx-2xy.b. The operation,* defined by
7. Let T be an element of L(R3) such that-4,5,"7" are it eigenvalues. show that T(x)-9x=(-4,5,"7" )