Question: True or False? Give a quick justification. (a) Given A E Mmxn (R), the function TA is a linear transformation from R to Rm. (b)

True or False? Give a quick justification. (a) Given A E Mmxn (R), the function TA is a linear transformation from R" to Rm. (b) T: R2 -> R2 defined by T a + 2y = is a linear transformation. y - 1 (c) Given a linear transformation T, if T(v) = T(-7) then U = 0. (d) If T : R3 - R2 is linear, then its standard matrix has size 3 x 2. (e) A linear transformation may have more than one standard matrix representation. (f) For any linear transformation, T = TITLE. (g) Let A E Mmxn(F). If TA is one-to-one, then the system Ax = b is consistent, for all b EFm . (h) TAP = TAP (i) Given the matrices A, B and C, if the product ABC is well defined, then To o TB o TA = TABC. (j) Given two linear transformation U and T, Ker(U . T) C Range(T)

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