Answers
Multiply on the right by the transpose of the matrix on the left side:
[tex]X\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}=\begin{bmatrix}-5&-1&0\\5&-2&5\end{bmatrix}[/tex]
[tex]X\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}^\top=\begin{bmatrix}-5&-1&0\\5&-2&5\end{bmatrix}\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}^\top[/tex]
The transpose is just the same matrix with the entries reflected along the main diagonal:
[tex]\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}^\top=\begin{bmatrix}1&3\\-1&0\\2&1\end{bmatrix}[/tex]
So
[tex]X\begin{bmatrix}1&-1&2\\3&0&1\end{bmatrix}\begin{bmatrix}1&3\\-1&0\\2&1\end{bmatrix}=\begin{bmatrix}-5&-1&0\\5&-2&5\end{bmatrix}\begin{bmatrix}1&3\\-1&0\\2&1\end{bmatrix}[/tex]
[tex]X\begin{bmatrix}6&5\\5&10\end{bmatrix}=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}[/tex]
Now multiply on the right by the inverse of the matrix on the left side:
[tex]X\begin{bmatrix}6&5\\5&10\end{bmatrix}\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}[/tex]
[tex]X=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}[/tex]
The inverse is
[tex]\begin{bmatrix}6&5\\5&10\end{bmatrix}^{-1}=\frac1{60-25}\begin{bmatrix}10&-5\\-5&6\end{bmatrix}=\begin{bmatrix}2/7&-1/7\\-1/7&6/35\end{bmatrix}[/tex]
So
[tex]X=\begin{bmatrix}-4&-15\\17&20\end{bmatrix}\begin{bmatrix}2/7&-1/7\\-1/7&6/35\end{bmatrix}=\boxed{\begin{bmatrix}1&-2\\2&1\end{bmatrix}}[/tex]
Related Questions
Geometry only answer if you know, Need help
Answers
These triangles are congruent under the SAS congruence criterion. The angles that face each other at the tip of these two triangles are vertically opposite angles, so their measures will be equal. It is already given that two sides of these two angles are equal. Since two sides and one included angle is equal, the SAS congruence criterion can be used to prove that this triangle is congruent.
Answer (b) :These triangles are congruent under the SSS congruence criterion. This criterion states that if all three sides of two triangles are equal then they are congruent triangles. Since two sides and one included/common side of these triangles are equal they can said to be congruent under the SSS congruence criterion.
Answer (c) :These triangles can be proved to be congruent using the SAS congruence criterion. Let us prove it using the following steps :
Given :
In triangle 1 :
Measure of an angle = 48°Measure of one of its side = 6 cmMeasure of another side = 6 cmIn triangle 2 :
Measure of an angle = 48°Measure of one it's side = 6 cmMeasure of another side = 6 cmSince two sides and one included angles of both these triangles are equal, we can conclude that they are congruent under the SAS congruence criterion.
Answer:
lady strange is the best
Step-by-step explanation:
Write the equation of the line that passes through the points (-1, 10) and (5, 2)
Answers
Answer:
[tex]y=-\frac{4}{3}x +\frac{26}{3}[/tex]
Step-by-step explanation:
1) if the point A has coordinates (-1;10) and the point B - (5;2), then it is possible to write common view of the required equation of the line:
[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};[/tex]
2) if to substitute the coordinates of A&B into the common equation, then:
[tex]\frac{x+1}{5+1} =\frac{y-10}{2-10}; \ => \frac{x+1}{6}=\frac{y-10}{-8};[/tex]
3) finally, in slope-intersection form:
3y= -4x+26; ⇔ y= -4/3 x +26/3.
P.S. the suggested way of the solution is not the only one.
When adding integers with the same sign, add the absolute values of the integers.
True or False?
Answers
Answer:
False. This only goes with integers that are both positive.
Step-by-step explanation:
For example, 7+6 is the same as |7|+|6|, which is, again, the same as 7+6.
However, when you add integers that are both negative, you're subtracting, and you'll always end up with a negative difference. Absolute values are always positive, which is why this doesn't work.
(-7)+(-6)
= -7-6
= -13
|-7|+|-6|
= 7+6
= 13
I hope this helps!
A 13 foot board is cut into 2 pieces, if one piece is x feet long express the other length in terms x
Answers
Answer:
if they are equal then it would be 6.5
What are the two steps used to solve a two-step equation?
Answers
2) Secondly, multiply or divide both sides of the linear equation by the same number.
3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable.
One number is 3 times as large as another. Their sum is 28. Find the numbers
Answers
Answer
7
Step-by-step explanation:
help me plsssssssssssssssssssssss!
Answers
"Answer" and Explanation:
All I can tell is that x=60, and that the angle is also 60, since it is and equalateral triangle. I can't see anything about sides lengths nor can I tell what 'side' means, so yeah that's all I can say. Sorry that probably didn't help at all.
Find o% of 176:
Find 100% of 176:
Find 50% of 176:
Find 25% of 176:
Find 75% of 176:
Answers
176
88
44
132
Hope this helps
Can anyone help me with this please....
[tex]2 \sin2x - \sin(x) . \sqrt{2ctgx} = 1[/tex]
Answers
2× - sin (×), √2xtg × ≈ 1 =
Tom bought a television and paid of the original price, including tax. The original price of the television was $500. How much change did
Tom receive if he paid the cashier $400?
A $25
B. $50
o C. $75
D. $150
Answers
The answer isn't in A. B. C. or D.
Step-by-step explanation:
The answer would be negative or not be in the answer list.
Plz I need help with these two
Answers
Answer:
x<=2
11>=x
Step-by-step explanation:
x+14<=16
x<=2
Which quadrilateral can be classified as a trapezoid?
Answers
Answer:
the forth one
Step-by-step explanation:
plz mark brainlest
The quadrilateral can be classified as a trapezoid should be considered in the figure 4.
What is a trapezoid?
It is treated as the quadrilateral in which there is one pair of the parallel of the opposite sides. It involved the right angles i.e. right trapezoid also have the congruent sides i.e. isosceles
So based on the given figure, we can say that The quadrilateral can be classified as a trapezoid should be considered in the figure 4.
Learn more about trapezoid here: https://brainly.com/question/2036345
A model boat is marked down 15% off the original price of $50. What is the sale price of the
boat?
Answers
Answer: $42.5
Step-by-step explanation: So first they take off 15% of of $50 so that means they took $7.5. And now its asking for the price of it after so $7.5-$50= $42.5.
Explanation:
jill bikes 15 miles in the morning anda 17 miles in the afternoon. how many miles does she bike in all?
Answers
Answer:
32 miles all together
Step-by-step explanation:
Jill bikes in the morning and in the evening as well, so the total distance covered by him is equal to 32 miles.
What is arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
Total distance travelled by Jill in the morning = 15 miles
Total distance travelled by Jill in the evening = 17 miles.
Then, the total distance covered by Jill will be,
D = 15 + 17
D = 32 miles
To know more about arithmetic operations:
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15 points and brainliest! Solve for x. 7x + 3 = 17
A: x= 2
B: x=7
C: x=20
D: x=27
Answers
Answer:
Its A
Step-by-step explanation:
7x + 3 =17
-3 ( 17 -3 = 14)
7x = 14. (14 divided by 7)
u get x=2
the cost of New York Yankees baseball cap is 24.00. The local sporting goods store sells it for $30.00. markup rate
Answers
I need help with this if you get it right I will mark you
Answers
Answer:
x=156Step-by-step explanation:
Set up equation:
29+x-5=180
Combine like terms:
24+x=180
Subtract 24 on both sides:
x=156The dot plots below show the age of some dance students and some yoga students: Two dot plots are shown one below the other. The top and the bottom plots have the title Dance Students and Yoga Students respectively. Below the line for each dot plot is written Age followed by years in parentheses. The markings on each line are from 10 to 30 at intervals of 1. For the top plot there are two dots for 13 and 16 and 1 dot each for 12, 15, 17, 18, and 20. For the bottom plot there are 2 dots for 25 and 1 dot each for 17, 19, 20, 22, 24, 27, and 29. Based on visual inspection of the dot plots, which group of students appears to have the larger average age? The yoga students The dance students Both groups are similar. Not enough information is available to draw a conclusion.
Answers
Answer:
The yoga students
Step-by-step explanation:
This one is kinda easy but i took the test and got it right have a good day! :)
Answer:
yoga students
Step-by-step explanation:
i did the math in math class for this question lol.
-7 es numero natural?
Answers
Answer:
no no es un numero natura,los numeros naturales son los que estan completos como el 1 el 2 el 3 y mas numeros los que son menos o con punto decimal no lo son
HELP IM GIVING 20 POINTS LIKE PLZZ I NEED HELP
Answers
Answer:
price = 4.1
cost = 12.3
Step-by-step explanation:
price = 0.8+1.2+1.5+0.6 = p4.1
cost = 2.40+3.60+4.50+1.80 = $12.3
please help appreciate it!!
Answers
Answer:
I only
Step-by-step explanation:
It is the only one that passes through both.
Desmos is a great graphing calculator
Answer:
the is answer is neither
Step-by-step explanation:
i also used desmos and i got neither.
what is the sum of 1/8 + 5/16 + 3/8
Answers
Answer:
0.8125
Step-by-step explanation:
because i did the process
Answer:
0.8333333 or 13/16
Step-by-step explanation:
Change 1/7 / 4/21 to a ratio?
Answers
Answer:
3:4
Step-by-step explanation:
(1/7)/(4/21) = (1/7)×(21/4) = 3/4 = 3:4
Please help cause my class over in a few mins please hurry
Answers
Answer:
3x+4
Step-by-step explanation:
just combine like terms
x+2x= 3x
3+1=4
Write the coordinates of the vertices after a reflection across the line x=-1
Answers
Answer:
U is (0,-8)
V is (0,-10)
T is (5,-8)
S is (5,(-10)
pleaseeeeeeeeeeee helpppppppppppppppp
Answers
Answer:
hirap naman yan basahin mo kasi directions
16. A photograph is reduced to 75% of its original size. The photo was originally 96 squaro Inches. What is
the now area after it has boon reduced?
Answers
Answer:
mom clock usualli a h i j o
Which point could be on the line that is parallel to line KL and passes through point M?
(–10, 0)
(–6, 2)
(0, –6)
(8, –10)
Answers
Answer:
D. (8, –10)
Step-by-step explanation:
(8, -10) passes through this line.
The correct option is D
What is Coordinate Geometry?
By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given data:
We are given a line KL in the diagram, and we have to find out which point out of the given options will satisfy the equation of the line which is parallel to KL and passes through M.
Using the intercept form equation of line KL:
x/a + y/b = 1 [a and b are x and y intercepts respectively]
x/6 + y/4 = 1
4x + 6y = 24
Slope of this line = -a/b = -4/6 = -2/3
The line parallel to this will have the same slope and should pass through (-4, -2)
y - (-4) = (-2)/3 [x - (-2)]
y + 4 = (-2/3)[x + 2]
3y + 12 = -2x - 4
2x + 3y + 14 = 0
Clearly (8, -10) passes through this line.
2(8) + 3(-10) + 14 = 0
Hence, (8, -10) passes through this line.
To learn more about Coordinate Geometry, click:
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Question 1) Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x - 3y = 13, x + 2y = -4. ( I'll post a picture of the question and problem incase there's any confusion). Will Mark Brainliest.
Answers
Answer:
x = 2 and y = -3
Step-by-step explanation:
The given equations are:
2x - 3y = 13 ...(1)
x + 2y = -4 ...(2)
Multiply equation (2) by 2.
2x + 4y = -8 ...(3)
Subtract equation (3) from (1).
2x - 3y-(2x + 4y) = 13-(-8)
2x-3y-2x-4y = 13+8
-7y = 21
y = -3
Put the value of y in equation (2).
x + 2(-3) = -4
x-6=-4
x = 6-4
x = 2
So, the solution of the given equations are x = 2 and y = -3.
Find the product. 5/8 of 24 A. 8 B. 15 C. 11 D. 9
Answers
Answer:
15 = B
Step-by-step explanation:
5/8 x 24 = 15
Step-by-step explanation:
5/9×24
5/8×24
[tex] \frac{5 \times 24}{1 \times 8} [/tex]
[tex] \frac{120}{8} [/tex]
B.15
hope it's helpful ❤❤❤❤
THANK YOU.