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djyliett [7]
3 years ago
15

Help please please please! WILL MARK BRAINLIST

Mathematics
1 answer:
Mashcka [7]3 years ago
7 0

Answer: I think it is A or B

Step-by-step explanation:

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Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is reflection over the line y=1/2x
trapecia [35]

Answer:

A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]

Step-by-step explanation:

We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.

Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).

On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have

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By summing the first vector with the double of the second one we get, using linearity

T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)

Hence, T(0,1) = (4/5,-3/5)

Now, we take the second vector and substract it the double of the first one (to kill the second variable)

T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)

Therefore, T(1,0) = (1,4/3)

The matrix A induced by  T has in its first column T(1,0) and in its second column T(0,1). We conclude that

A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]

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Step-by-step explanation:

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Round to the nearest tenth :14.94<br><br> need answer ASAP, please explain your answer!
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14.9


Step-by-step explanation:


Here’s a trick 5 or more let it sore 4 or less let it rest.
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A small pebble has a mass of<br> about<br> 20 L<br> b.<br> 20 ml<br> 20 g<br> 20 kg<br> d.
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