Question

(a) Let T be any linear transformation from R2 to R2 and v be any vector...

(a) Let T be any linear transformation from R2 to R2 and v be any vector in R2 such that T(2v) = T(3v) = 0. Determine whether the following is true or false, and explain why: (i) v = 0, (ii) T(v) = 0.

(b) Find the matrix associated to the geometric transformation on R2 that first reflects over the y-axis and then contracts in the y-direction by a factor of 1/3 and expands in the x direction by a factor of 2.

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