Recall that the standard basis of ℝ3 is {E1, E2, E3}. If T:ℝ3→ℝ2 is a transformation and the action of T on the vectors Ei is as
given, find a formula for T(X), where X is any vector in ℝ3.
T(E1)= 2 T(E2)= \begin{bmatrix} 0 \\ 5 \end{bmatrix} T(E3) = \begin{bmatrix} 4 \\ 0 \end{bmatrix}
T\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} ? \\ ? \\ ? \end{bmatrix}
T(E1)= 2 T(E2)= \begin{bmatrix} 0 \\ 5 \end{bmatrix} T(E3) = \begin{bmatrix} 4 \\ 0 \end{bmatrix}
T\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} ? \\ ? \\ ? \end{bmatrix}
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Check the picture below.
is not very specific above, but sounds like it's asking for an equation for the trapezoid only, mind you, there are square tiles too.
but let's do the trapezoid area then,
![\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20a%5E%7B%5Cfrac%7B%7B%20n%7D%7D%7B%7B%20m%7D%7D%7D%20%5Cimplies%20%20%5Csqrt%5B%7B%20m%7D%5D%7Ba%5E%7B%20n%7D%7D%20%5Cqquad%20%5Cqquad%0A%5Csqrt%5B%7B%20m%7D%5D%7Ba%5E%7B%20n%7D%7D%5Cimplies%20a%5E%7B%5Cfrac%7B%7B%20n%7D%7D%7B%7B%20m%7D%7D%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
is not very specific above, but sounds like it's asking for an equation for the trapezoid only, mind you, there are square tiles too.
but let's do the trapezoid area then,