I have worked out a transformation problem and assembled a matrix. I have shown my work on the transformation and created matrix in the attached file. At the end of my work I have five (5) short theory questions about subspaces and dimension. Please see attached file.

Subspace and dimension are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

... that ( 8) We have to check now the 3x3 matrices. ... by the vectors containing the non-singular matrix of above ... of these functions denoted as W is a subspace of P2 ...

... Ax||<= |A||*||x||, so if a sequence of matrices converges B_i ... Then, given a matrix A, it is proved that a linear ... of n . Show that E is a closed subspace of n ...

... is a subspace, since the sum of diagonal matrices is diagonal ... product of a scalar to a diagonal matrix is diagonal ... iii) It is a subspace, since the sum of upper ...

... This has 2 pivot columns, so the dimension of the ... 2/. Solution: The projection onto the subspace is the ... dependent since the determinant of the matrix is zero. ...

... space over K and let A = EndK(V), the ring of n n matrices over K ... and A are the only 2-sided ideals of A, so that matrix rings are ... 1. Let be a subspace of ...

... U1+U2 = V. Prove that there is a subspace W of ... 1) Consider the given vectors as row matrices. Write down the echlon matrix whose rows include the given vectors ...

Linear Transformations, Matrices, Orthogonal Projections. ... The diagonalizing matrix is simply the matrix composed of the ... 1 , x 2 , x 3 xp } for subspace W of ...

... Explain the relationship between or thogonal matrices and isometries ... Find a, b and c such that the matrix 1/3 ... 4 (c) Let V be a subspace of R deﬁned by. ...

... K and let A = EndK(V), the ring of nxn matrices over K ... The ring is clearly Artenian since it has finite dimension over K ... either (0) or A. Let W be a subspace of V ...