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Question: linear algebra find the standard matrix for these linear transformations...

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Linear Algebra. Find the standard matrix for these Linear Transformations:

1.) The dot product, (t) = u . g . Assume er U1, V2,....Vn so that you may compute (t) = u . g by multiplying vec{v} by a matrix on the left.

2.) The cross product, so for Fixed UE We , define C_{vec{w}}:mathbb{R}^{3} ightarrow mathbb{R}^{3} by C_{vec{w}}(vec{v})=vec{v}otimes vec{w} which is linear. Find the standard matrix for C_{vec{w}} , assume vec{w}=(w_{1},w_{2},w_{3})^{T} .

3.) T:mathbb{P}_{3} ightarrow mathbb{P}_{2} given by Tf(x)=f'(x). Use the standard basis {1,x,x2,...,xn} for mathbb{P}_{n}.

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