Properties of Matrix Transformations Theorem 4.9.1: For every matrix
... Theorem 4.9.2: If TA : Rn → Rm and TB : Rn → Rm are matrix transformations, and if TA (x) = TB (x) for every vector x in Rn , then A=B. Given a matrix transformation we can find the matrix representing the transformation Standard Matrix for a matrix transformation: Let T : Rn → Rm be a matrix transf ...
... Theorem 4.9.2: If TA : Rn → Rm and TB : Rn → Rm are matrix transformations, and if TA (x) = TB (x) for every vector x in Rn , then A=B. Given a matrix transformation we can find the matrix representing the transformation Standard Matrix for a matrix transformation: Let T : Rn → Rm be a matrix transf ...
Homework 9 - Solutions
... We see that any vector ~x ∈ V is a linear combination of ~v1 , ~v2 , so that V = Span(~v1 , ~v2 ). We have seen that an m-dimensional subspace (of Rn ) has at most m linearly independent vectors. Since there are 2 linearly independent vectors in V (which is a subspace of R3 ), it must have dimensio ...
... We see that any vector ~x ∈ V is a linear combination of ~v1 , ~v2 , so that V = Span(~v1 , ~v2 ). We have seen that an m-dimensional subspace (of Rn ) has at most m linearly independent vectors. Since there are 2 linearly independent vectors in V (which is a subspace of R3 ), it must have dimensio ...
