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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Related Questions
The complement of an angle is 59°. What is the measure of the angle?
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Tropical Storm Zeta will bring 0.36 in. of rain to New Orleans. Which fraction is equivalent to this amount of rain in inches?
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Answer: 9/25 inches of rain
Step-by-step explanation: Put the decimal (0.36) over its place value (100), which turns it into 36/100. Now, simplify by dividing the numerator (36) and the denominator (100) by the greatest common factor (4), to get the answer 9/25.
a baseball player got 13 hits in 50 times at bat. what percent of her times at bat did she get a hit
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Answer:
26%
Step-by-step explanation:
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Step-by-step explanation:
What single principal deposit is needed?
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Answer:
It’s C
Step-by-step explanation:
You can use the formula A = 252 + 4sh to find the surface area of a square prism
that has a base with edge length s and height h. A square prism has a base with
edges that are 12 centimeters long and a height of 15 centimeters. What is the
surface area of the square prism? Show your work.
Please answer fast!! I’m in a test. Give the full explanation
Answers
Answer:
The surface area is 972 square cm
Step-by-step explanation:
Numeric Value of Functions
Given the function:
A = 252 + 4sh
Where A is the surface area of a square prism , s is edge length of the base h is the height.
A square prism has a base with edges s=12 cm long and height of h=15 cm.
Substituting these values, we get:
A = 252 + 4(12)(15)
A = 252 + 720 = 972
A = 972
The surface area is 972 square cm
The surface area of the square prism is 1008 cm².
Surface area of a square prism:
Surface area = 2s² + 4shwhere
s = edge side
h = height
Therefore,
s = 12 cm
h = 15 cm
surface area = 2 × 12² + 4 × 12 × 15
surface area = 2 × 144 + 48 × 15
surface area = 288 + 720
surface area = 1008
surface area = 1008 cm²
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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.
Answers
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
49.05 / 7 = 7.00 (Rounded)
I tried my best to solve this, sorry if it doesn't help.
Please help!! ASAP!!!
Answers
Answer:
125 cm
Step-by-step explanation:
I am 100% sure because I did the math
what does n equal? btw this is 6th grade! also < Is between 3 and 5
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!!!
Luke earned a grade of 88% on his multiple choice history final that had a total of
200 problems. How many problems on the final exam did Luke answer correctly?
Answers
Answer:
176
Step-by-step explanation:
88% = 88/100
88 × 2 = 176
176/200
Answer:
176 is the answer
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
Answers
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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A car travels about 25 miles on one gallon gas.if between 10 and 12
Gallons of gas are used
Answers
Answer:
The car will travel between 250 and 300 miles with a consumption of between 10 and 12 gallons of gasoline.
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:
1 = 25
10 = X
((25 x 10) / 1) = X
250 = X
So if you use 10 gallons of gasoline, the car will travel about 250 miles. Now if you use 12 gallons, it will go about 300 miles.
Therefore, the car will travel between 250 and 300 miles with a consumption of between 10 and 12 gallons of gasoline.
What is the distance between point A and point C on the number line?
А
8
B
10
с
5
D
6
Answers
10 units is the distance between point A and point C on the number line.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the distance between point A and point C on the number line.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
The length along a line or line segment between two points on the line or line segment is known as distance.
The point A is at -3.
The point C is at 7
Now the distance between A and C is AC.
AC=OC-OA
=7-(-3)
=7+3
=10
Hence, 10 units is the distance between point A and point C on the number line.
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need help fast
The graph of y^2 + 8y – 4x – 24 = 0 is a parabola. Where is the focus located?
Answers
Answer:
It’s (-9,-4)
Step-by-step explanation:
Edge
The focus of the graph of the function is located at (−9,−4).
Given that, the graph of y²+ 8y – 4x – 24 = 0 is a parabola. We need to find where is the focus located.
What is vertex form?The vertex form of an equation is an alternate way of writing out the equation of a parabola. Normally, you'll see a quadratic equation written as ax²+bx+c, which, when graphed, will be a parabola.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Right
Vertex: (−10, -4)
Focus: (-9, -4)
Axis of Symmetry: y=−4
Directrix: x=−11
Therefore, the focus of the graph of the function is located at (−9,−4).
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4.
What is the result of (f X g)(x) if
f(x) = -3x + 11 and g(x) = 11x + 7?
( 33x² 100x - 77
(B 33x - 142x - 77
C -33x + 100x + 77
D -33x² + 142x + 77
Answers
Answer:
thank you
Step-by-step explanation:
thanks for the pts i need them sowwy
Find the angle PQR [Geometry]
Answers
Answer:
5⁰
Step-by-step explanation:
Angle on A STRAIGHT line sums up to 180⁰
angle PQR and angle RQS are both on a straight line therefore they sum up to 180⁰
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divide both sides by 9
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Answers
Answer:
y=-4x+14
Step-by-step explanation:
A parallel line must always have the same slope, so it must be -4x, and on a graph y=-4x+14 passes through the point (4,-2)
A man flies a small airplane from Fargo to Bismarck, North Dakota- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1.2 hours. What is the planes speed in still air, and how fast is the wind blowing?
1) His plane speed equals ______ mph
2) The wind speed equals ______ mph
Answers
Answer:
1.) 120 mph
2.) 30 mph
Step-by-step explanation:
Given that a man flies a small airplane from Fargo to Bismarck, North Dakota- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1.2 hours. What is the planes speed in still air, and how fast is the wind blowing?
Let the wind speed = w
and the plane speed = p
From the first sentence,
P - w = 180/ 2
P - w = 90 ....... ( 1 )
From the second statement,
P + w = 180/1.2
P+ w = 150 ...... ( 2 )
Solve equation 1 and 2 simultaneously
P + w = 150
P - w = 90
Add the two equations
2P = 240
P = 120 mph
Substitute p in equation 1
W = 150 - 120
W = 30
Therefore, the wind speed is 30 mph and the plane speed is 120 mph
can someone explain what surface area means?
Answers
Answer:
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Step-by-step explanation:
The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all 6 faces added together
276.2 rounded to the nearest tenth
Answers
Answer:
276.2 rounded to the nearest 10th is 276.2.....
Step-by-step explanation:
Answer:276.2...
Step-by-step explanation:
Divide. 5,346 ÷ 29 Enter your answer in the boxes as a mixed number in simplest form.
Answers
Answer:
[tex]190\frac{26}{29}[/tex]
Step-by-step explanation:
____190__
29 | 5346
-29 (29*100=2900)
________
2446
-232 (29*90=232)
________
26
Therefore, the answer is [tex]190\frac{26}{29}[/tex]
In the mixed form we can write → 5346 ÷ 29 as [tex]$184\frac{10}{29} .\\[/tex]
We have the following operation -
5346 ÷ 29
We have to write the result of above division in mixed form.
What is Division Algorithm ?The division algorithm says when a number 'a' is divided by a number 'b' gives the quotient 'q' and the remainder 'r' then the following relation exists-
a = bq + r
where 0 ≤ r < b.
This is also known as Euclid's division lemma.
According to the question, we have -
5346 ÷ 29
Let A = 5346 ÷ 29. Therefore -
A = [tex]$\frac{5346}{29} = 184\frac{10}{29} .\\[/tex]
Hence, in the mixed form we can write → 5346 ÷ 29 as [tex]$184\frac{10}{29} .\\[/tex]
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Can someone please help my brain can’t process information anymore
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Answer:
A day because within a day Chris bags left is 6 and evans too 6 bags left
The center of a circle is located at the point (1,1). The point (6,3) is located on the circle.
What is the radius of the circle?
Answers
Answer:
Square root of 29
Step-by-step explanation:
The required radius of the circle would be √29 units which circle with a center at (1, 1) and a point on the circle is (6, 3).
What is the equation of a circle?The equation of a circle with center (h,k) and radius r is :
r² = (x−h)² + (y−k)²
Given that a circle with a center at (1, 1) and a point on the circle is (6, 3).
Since the circle passes through points (6, 3),
So the radius (r) of the circle is the distance between points (1, 1) and (6,3).
⇒ r² = (6 - 1)² + (3 − 1)²
⇒ r² = (5)² + (2)²
⇒ r² = 25 + 4
⇒ r² = 29
⇒ r = √29
Therefore, the required radius of the circle would be √29 units.
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Work out the value of (√5)^2 x (√3)^2?
Answers
Explanation
Any root, squared, equals its non-square root number sqrt 5 ^ 2 = 5
What do the rhombus and the parallelogram shown below have in common?
O Only opposite angles are congruent.
O Only opposite sides are parallel.
O All sides are congruent.
O Both opposite sides and opposite angles are congruent.
Answers
Answer:
Your Answer is D, Both opposite sides and angles are congruent
Step-by-step explanation:
I'm just going to write a load of BS here to see if i cant get the answer to show up so all of you wonderful people don't have to waste so much time on watching a video, so instead you can get your answer for free, and also for a proper explanation I looked this question up, didn't fund anything so I guessed and got it correct, hope this helped.
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D
Step-by-step explanation:
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I think it must be between 75 and 76
What is the value of the exponential expression below 64 1/2
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Answer:
its 8
Step-by-step explanation:
Help, asap lol I forgot what it was and didn't take notes.
problem in photo attached ^.^
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Answer:
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Step-by-step explanation:
hi I need to know this do u think u can help 5/6 + 3/4 + 2/3
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Answer:
2 1/4
Step-by-step explanation:
Mandy and her mom are making homemade play-dough. Besides the flour, the recipe calls for 1/4 cup of salt for every 3/4 cup of water
used. How much salt would they need if they used one cup of water?
Answers
Answer:
about a half teaspoon
Step-by-step explanation: