Find the matrix A of the reflection in the line L in R2 that consists of all scalar multiples of the vector.
Answers
Answer:
hello your question is incomplete attached below is the complete question
answer : 2/13 6/13
6/13 3/13
Step-by-step explanation:
Firstly we will calculate the orthogonal basis L in R^2
attached below is the detailed solution
also assuming β to be the standard ordered basis
hence the matrix A of the reflection in the Line L in R2 =
2/13 6/13
6/13 3/13
The matrix A of the reflection in line L is given by [tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex] and this can be determined by first evaluating the value of [tex]\rm R^2[/tex] by using the given data.
The orthogonal basis L in [tex]\rm R^2[/tex] is given by:
[tex]r = [u_1,u_2] =\left[\dfrac{1}{\sqrt{39} }\binom{6}{3}, \dfrac{1}{\sqrt{39} }\binom{3}{-6}\right][/tex]
[tex]\rm T(u_1)=u_1[/tex]
[tex]\rm T(u_2)=0[/tex]
[tex]\rm [T]_r = \begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}[/tex]
[tex]\rm Q = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]
Now, matrix A is given by the formula:
[tex]\rm A=Q[T]_rQ^{-1}[/tex]
Now, substitute the value of known terms in the above equation.
[tex]\rm A = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}\dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]
Simplify the above expression.
[tex]\rm A = \dfrac{1}{{39} }\begin{bmatrix}6 & 18\\ 18 & 9\end{bmatrix}[/tex]
[tex]\rm A = \dfrac{3}{{39} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]
[tex]\rm A = \dfrac{1}{{13} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]
Multiply by 1/13 in the matrix.
[tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex]
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Answers
Answer:
[tex]190\frac{26}{29}[/tex]
Step-by-step explanation:
____190__
29 | 5346
-29 (29*100=2900)
________
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________
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Therefore, the answer is [tex]190\frac{26}{29}[/tex]
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This is also known as Euclid's division lemma.
According to the question, we have -
5346 ÷ 29
Let A = 5346 ÷ 29. Therefore -
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Hence, in the mixed form we can write → 5346 ÷ 29 as [tex]$184\frac{10}{29} .\\[/tex]
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Edge
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
If a car travels 25 miles on a gallon of gasoline, when using between 10 and 12 gallons of gasoline, the miles it will travel are derived from the following calculation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
176
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If you are able to answer this I’ll give most Brainly and I need it in about 20 min
Nov
Month June July Aug Sept Oct
Rainfall (in.) 6.14 7.19
8.63
8.38 6.47
2.43
2. The table shows monthly rainfall in inches for
five months. Identify the outlier in the data set.
Determine how the outlier affects the mean,
median, and mode of the data. Then tell which
measure of center best describes the data with
and without the outlier. Round to the nearest
hundredth. Justify your selection.
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okay, first to figure out the IQR of the table you need to organize them from least to greatest.
2.43, 6.14, 6.47, 7.19, 8.38, 8.63
to find the middle number of all of these you add them all together and divide by 6, which is the total amount of numbers there.
2.43 + 6.14 + 6.47 + 7.19 + 8.38 + 8.63 = 39.24
39.24 / 6 = 6.54
now that we have the IQR, next we find the outlier. to find the outlier you multiply the IQR by 1.5 which is 6.54 x 1.5 = 9.81 <- outlier
Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.
2.43 + 6.14 + 6.47 + 7.19 + 8.38 + 8.63 + 9.81 = 49.05
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I tried my best to solve this, sorry if it doesn't help.
AE is an angle bisector of BAC if the measure of BAE = x + 30 and masure of angle EAC = 3x-10 determine Measure of angle EAC
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The value of x for the given geometry will be 20°.
What is an angle?The angle is the measurement of the angular distance. For instance, we have a meter and an inch for linear motion, but we don't have a measurement for angular rotation, therefore the angle is helpful in determining angular rotation.
An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Given that AE is a bisector of ∠BAE and ∠EAC
so,
∠BAE = ∠EAC
x + 30 = 3x - 10
x = 20°
Hence 20° will be the answer to the given question.
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Answers
Answer:
n < 4
Step-by-step explanation:
[tex]\frac{1}{2} n+3<5[/tex]
-3 -3
[tex]\frac{1}{2} n[/tex] < 2
divide both sides by [tex]\frac{1}{2}[/tex]
n < 4
Hope this helps!!!