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Callmetay24
04.11.2020 •
Mathematics
Let e1= 1 0 and e2= 0 1 , y1= 4 5 , and y2= −2 7 , and let T: ℝ2→ℝ2 be a linear transformation that maps e1 into y1 and maps e2 into y2. Find the images of 4 −4 and
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Ответ:
The image of
through T is ![\left[\begin{array}{c}24&-8\end{array}\right]](/tpl/images/0866/6174/8333b.png)
Step-by-step explanation:
We know that![T:](/tpl/images/0866/6174/5c4e0.png)
→
is a linear transformation that maps
into
⇒
And also maps
into
⇒
We need to find the image of the vector![\left[\begin{array}{c}4&-4\end{array}\right]](/tpl/images/0866/6174/b8b65.png)
We know that exists a matrix A from
(because of how T was defined) such that :
We can find the matrix A by applying T to a base of the domain (
).
Notice that we have that data :
Being
the cannonic base of ![IR^{2}](/tpl/images/0866/6174/a2328.png)
The following step is to put the images from the vectors of the base into the columns of the new matrix A :
Writing the matrix A :
Now with the matrix A we can find the image of
such as :
We found out that the image of
through T is the vector ![\left[\begin{array}{c}24&-8\end{array}\right]](/tpl/images/0866/6174/8333b.png)
Ответ:
x | y
-2 | -7
0 | 1
2 | 9
4 | 17
step-by-step explanation: