Linear Transformatio Word Scramble
|
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Question | Answer |
Linear Transformation | Let V & W be two vectors spaces. A map T frm V to W. |
Linear Transformation from Rn to Rm is of the form ... | T(x) = Ax with A= [T(e1):T(e2):...:T(en)] |
Ck(I) | Space of continuous function on the I interval |
Mapping T:(V -W) with V and W be vector spaces | T from V onto W is a rule that assigns to each vector v in V precisely one vector w=T(v). |
Linearity properties | T(u+v) = T(u) = T(v) for all u,v in V T(cv) = cT(v) for all v in V and all scalars c. |
A mapping T:V-W is called ilnear transforamtion from V to W if .... | Linear Properties are true. The vector space V is called the domain of T, whie the vector space W is called the codomain of T. |
Let T:V-W be a linear transformation. Then ... | T(0v) = 0w T(-v) = -T(v) for all v in V. |
A linear transformation T:Rn - Rm defined by T(x) = Ax is an m x n matrix called ...; | Matrix Transformation |
Ker (T) = | {v in V: Tv = 0} |
Ran ( T) = (or Rng(T)) | {T(v) of W : v in V} |
Kernel | Let T:V-W be a linear transforamtion.the set of all vector v in V such that T(v)=0 |
Range | A linear transformation T:V-W , the subset of W consisting of all transformed vector from V. |
If T:Rn-Rm is the linear transformation with matrix A, then ... | Ket(T) is the solution set to the homogeneous linear system Ax=0. |
If T:Rn - Rm with m x n matrix A , then Ket(T) = | nullspace(A) subspace of Rn |
If T:Rn - Rm with m x n matrix A , then Ran(T) = | colspace (A) subspace of Rm |
If T:V-W is a linear transformation, then Ker(T) = | is a subspace of V |
If T:V-W is a linear transformation, then Ran(T) = | subspace of W |
General Rank-nullity theorem | dim[Ran(T)] + dim[Ker(T)] = dim[V] |
Created by:
DrMolina
Popular Math sets