Consider that we have a given standard matrix of T and we are asked to find the image T(X) where X is a given vector. T is 4x3 and X is 3x1. is the solution of T(x) simply T*X?
2026-04-09 13:19:57.1775740797
Linear Transformation Concept Question
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Yes. If a basis is fixed, and you express $T$ and $x$ as matrices in terms of that basis, then $T(x)=T*x$ with matrix multiplication.
If you change bases, then the matrices in which $T$ and $x$ are expressed are probably going to change, but the result will still be computed with matrix multiplication, and it will yield the same result as $T(x)$.