Please Answer 1. Let T be a one-to-one, onto linear transformation from V into W. Show that Tis also a linear transformation andspecify the domain and range of this linear transformation.2. Let {V1,V2,.,Vn} be a basis for an inner product space V and suppose VEV is orthogonal to every vector in thisbasis. Show that V= 0.3. Suppose 0 is an eigenvalue of a matrix A. Show that A is not invertible by arguing from the point of view of thehomogeneous linear system with coefficient matrix A and invoking the equivalence theorem. Be very careful withdefinitions.4. Suppose V1,V2, V 3 are eigenvectors of a matrix A corresponding to distinct eigenvalues A1,12,13. Show thatV1,V2,V3 must be linearly independent.5. Let T be a linear transformation. Show that ker(T) is a subspace. State if it's a subspace of domain or range.

Name: Please Answer 1. Let T be a one-to-one, onto linear transformation fro
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please Answer 1. Let T be a one-to-one, onto linear transformation from V into W. Show that Tis also a linear transformation andspecify the domain and range of this linear transformation.2. Let {V1,V2,.,Vn} be a basis for an inner product space V and