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## Main Question or Discussion Point

let's consider we have a linear transformation T: R^2->R^3 and alpha={ordered basis of R^2} and beta{ordered basis of R^3} and gama={v1,v2}, v1=(1,-1),v2=(2,-5). now I need to find [T]_gama(associated matrix)? When i read about it, i understood it as, first we have to find transformation of each of the vectors from gama, [T(v1) , T(v2)] and write T(v1),T(v2) as linear combination of gamma vectors. The coeff. written in column would give me [T]_gamma.

I want to know whether what i have understood is right or wrong? and moreover i want to know why we need different forms [T]_(alpha/beta/gama) ?

I want to know whether what i have understood is right or wrong? and moreover i want to know why we need different forms [T]_(alpha/beta/gama) ?