Question

If T:V3 – V2 is a LT then​

Answer 1

Answer:

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Answer 2

Given:

If T:V3 -> V2 is a LT then

Solution:

given that-

$T:V^3 \rightarrow V^2$ is a LT (linear transformation) then,

According to definition of Linear transformation;

Let V^3 and V^2 be a vector space having different dimensions and let T be a function with domain V63 and range in V^2 defined as $T:V^3 \rightarrow V^2$.

Then, T is a linear transformation (LT) if

(a) - For all x, y ∈ V^3, $T(x+y)=T(x)+T(y)$ ,

T is additive.

(b) - For all x ∈ V^3 , r∈ $R$ , $T(rx)=rT(x)$

T is homogeneous.

Hence, If $T:V^3 \rightarrow V^2$ is LT then T is additive and homogeneous.