# Answer to Question #46067 in Linear Algebra for jasvinder

Question #46067

Let T : R^2 -> R^2 and S: R^2 -> R^2 be linear operators defined by

T ( x(subscript1) , x(subscript2) ) = (x(subscript1) + x(subscript2) , x(subscript1) - x(subscript2)) and S( x(subscript1) , x(subscript2) ) = ( x(subscript1) , x(subscript1) + 2x(subscript2) )

respectively.

i) Find ToS and SoT.

ii) Let B ={ (1;0) , (0;1) } be the standard basis of R^3. Verify that

[ToS](subscriptB) = [T](subscriptB) o [S](subscriptB).

T ( x(subscript1) , x(subscript2) ) = (x(subscript1) + x(subscript2) , x(subscript1) - x(subscript2)) and S( x(subscript1) , x(subscript2) ) = ( x(subscript1) , x(subscript1) + 2x(subscript2) )

respectively.

i) Find ToS and SoT.

ii) Let B ={ (1;0) , (0;1) } be the standard basis of R^3. Verify that

[ToS](subscriptB) = [T](subscriptB) o [S](subscriptB).

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