Q#1 Let T,: R2 R be the linear operators given by the formulas T,(x, y)...

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Q#1 Let T,: R2 → R² be the linear operators given by the formulas T,(x, y) = (x + y, x- y), T,(x, y) = (2x + y,x - 2y) (a) Show that T and T2 are one to one. (b) Find formula for T (x,y), T (x, y) and (T20T1)(x, y). (c) Verify (T, T,)-' = T,1oT;". Q#1 Let T,: R2 → R² be the linear operators given by the formulas T,(x, y) = (x + y, x- y), T,(x, y) = (2x + y,x - 2y) (a) Show that T and T2 are one to one. (b) Find formula for T (x,y), T (x, y) and (T20T1)(x, y). (c) Verify (T, T,)-' = T,1oT;".