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Let T R2 - R2 be a linear transformation, with associated standard matric A. That is (?1,e2) is the standard basis of R2. Suppose B is any basis for R2. T(5)]e = A[vje, where E = (1) Find a matrix B such that [T()B = BB. This matrix is called the the B-matrix of T and is denoted by T8, so A = [T\e is just the E-matrix of T. (2) What is the first column of [T\B. (3) Determine whether the following statements are true or false, and justify your answers (a) There exists a basis B of R2 such that [T\B (b) If T is the reflection about a line l through the origin in R2, then there exists a basis B for diagonal for any T : R2 ->R2. R2 such that TB is

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Let T: R^2 rightarrow R^2 be a lines transforms costs standard matrix A standard but for R^2 i.e 1_cy = A 1) now take any basis B for R^2 B = {b_1, b

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