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LetL: R' _ R2 be the linear transformation for which L(0,-2,4)-=(-1,21,L(2,0,11-(3,-2/, L(3,3,01-(4,-1) Find L(x,y,2}....

Question

LetL: R' _ R2 be the linear transformation for which L(0,-2,4)-=(-1,21,L(2,0,11-(3,-2/, L(3,3,01-(4,-1) Find L(x,y,2}.

LetL: R' _ R2 be the linear transformation for which L(0,-2,4)-=(-1,21,L(2,0,11-(3,-2/, L(3,3,01-(4,-1) Find L(x,y,2}.



Answers

Determine the linear transformation $T: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ that has the given matrix. $$A=\left[\begin{array}{r} -3 \\ -2 \\ 0 \\ 1 \end{array}\right]$$.

So this office problem we first have to observe that are matrix has 12345 columns. Which means we need to multiply this matrix by a five by one matrix of indeterminate variables, which were going to be X one next to x three next four. The next five, which are gonna be our indeterminate variables and doing the calculations we're going it gets x one minus four times next to minus six times x three plus zero times x four plus two times x five and translating this into a linear transformation. We're going to get okay T of x one common x two Common x three on the X four Colin x five Going to give us next one minus four times x 2 96 times x three plus two times x five

So this all this problem? First note that this matrix only has to calm. So we only need to multiply this matrix by a two by one matrix of indeterminate variables. Which is going to be x one x two which is going to give us when multiplied x one plus three x two and minus four x one was seven times x two And translating into linear intra linear transformation is gonna is gonna be TF x one comma next two is equal to x one plus three times x two comma minus four times X one seven times Next.

So to solve this problem, we first have to observe that are Matrix A has some three columns, which means we have to multiply it by a three by one matrix of indeterminate variables, which will look like this next one next to the next three as our indeterminate variables. So then computing remote location. We get two times x one plus two times x two minus three times X three four times X warn minus one times X two plus two times x three and five times x one plus seven times x two Minus date times extra. Translating this into a linear transformation we get t of x one next to kind of x three is equal to two times x one plus two times x two minus three times x three COMMA four times x one minus one times x two plus two times Next three comma five times x one plus seven times x two minus eight types extreme

But to solve this problem first note that our Matrix A has three columns, which means we need to multiply our matrix A by a major three by one matrix of indeterminate variables, which is going to be X one next to X ray. And so this will give us two x one minus. Next to plus five times x three and three x one plus x two, plus three times back. Three. Translating this into Okay, then your transformation and this will give us TF x one Conlan TMX two gxf three is equal to two times except one minus x two. Was five times x three comma three times x one plus x two plus three times x ray.


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