Let T : R2 → R3 be a linear transformation such that T( e⃗1 ) =...

Let T : R2 → R3 be a linear transformation such that T( e⃗1 ) = (2,3,-5) and T( e⃗2 ) = (-1,0,1).

Determine the standard matrix of T.
Calculate T( ⃗u ), the image of ⃗u=(4,2) under T.
Suppose T(v⃗)=(3,2,2) for a certain v⃗ in R2 .Calculate the image of ⃗w=2⃗u−v⃗ .

4. Find a vector v⃗ inR2 that is mapped to ⃗0 in R3.

Expert Solution

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Colby Messinger answered 2 years ago

Let T: R2 -> R2 be a linear transformation defined by T(x1 , x2) = (x1...

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Prove the following T is linear in the following definitions (a) T : R3 →R2 is...

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