Q#1 Let T,: R2 → R² be the linear operators given by the formulas T, (х, у) %3D (х + у,х — у), T2(x, y) = (2x + y, x – 2y) (a) Show that T, and T2 are one to one. (b) Find formula for T¡ (x,y), Tz²(x,...

Q#1 Let T,: R2 → R² be the linear operators given by the formulas<br>T, (х, у) %3D (х + у,х — у),<br>T2(x, y) = (2x + y, x – 2y)<br>(a) Show that T, and T2 are one to one.<br>(b) Find formula for T¡ (x,y), Tz²(x, y) and (T20T1)~(x, y).<br>(c) Verify (T,oT,)-1 = T,%oT;'.<br>

Extracted text: Q#1 Let T,: R2 → R² be the linear operators given by the formulas T, (х, у) %3D (х + у,х — у), T2(x, y) = (2x + y, x – 2y) (a) Show that T, and T2 are one to one. (b) Find formula for T¡ (x,y), Tz²(x, y) and (T20T1)~(x, y). (c) Verify (T,oT,)-1 = T,%oT;'.

Jun 05, 2022

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Q#1 Let T,: R2 → R² be the linear operators given by the formulas T, (х, у) %3D (х + у,х — у), T2(x, y) = (2x + y, x – 2y) (a) Show that T, and T2 are one to one. (b) Find formula for T¡ (x,y), Tz²(x,...

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