Let A be a 3×2 matrix, L its left inverse, and R its right inverse. L and R are then matrices such that LA = I₂ (the 2×2 identity matrix) and AR = I₃ (the 3×3 identity matrix). Clearly L must be 2×3 and R must be 3×2 in order for the matrix products to be defined.
To find L and R, we start by introducing a square matrix on the the left sides of either equation above. In particular, we uniformly multiply both sides by the transpose of A, then solve for the inverse.
For the left inverse, we have
[tex]LA=I[/tex]
[tex](LA)A^\top = IA^\top[/tex]
[tex]L\left(AA^\top\right) = A^\top[/tex]
[tex]\left(L\left(AA^\top\right)\right)\left(AA^\top\right)^{-1} = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]L\left(\left(AA^\top\right)\left(AA^\top\right)^{-1}\right) = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]LI = A^\top \left(AA^\top\right)^{-1}[/tex]
[tex]L = A^\top \left(AA^\top\right)^{-1}[/tex]
We do the same thing for the right inverse, but take care with how we multiply both sides of AR = I₃.
[tex]AR=I[/tex]
[tex]A^\top(AR)=A^\top I[/tex]
[tex]\left(A^\top A\right)R = A^\top[/tex]
[tex]\left(A^\top A\right)^{-1} \left(\left(A^\top A\right)R\right) = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]\left(\left(A^\top A\right)^{-1} \left(A^\top A\right)\right) R = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]IR = \left(A^\top A\right)^{-1} A^\top[/tex]
[tex]R = \left(A^\top A\right)^{-1} A^\top[/tex]
10+ Points)
Which is the graph of a proportional relationship?
Answer:
A
Step-by-step explanation:
The graph representing a proportional relationship is a straight line graph passing through the origin.
This is shown in graph A
Find 1 2··31 1 22 1··22. Show your work
1 = 1 = 1 < 2 < 22
1 is equal to 1 is equal to 1 is less than 2 is less than 22
1 = 1 =1 < 2 < 22 1 1 1 1 1 hope help mark brain.....?
Please help I don’t understand
Answer:
The value of x so f (x) = 7 is 5.
Step-by-step explanation:
Evaluate $\frac{20}{101}-\frac{20}{99}$. Express your answer in simplest form.
find the gradient and y- intercept of the line with equation 2x+3y-7=0
Answer:
Gradient = -2/3
y-intercept = 7/3
Step-by-step explanation:
Convert the equation in y = mx + c form, m is the gradient and c is the y-intercept
2x + 3y = 7
3y = -2x + 7
y = -2/3x + 7/3
The 66-mm-diameter solid shaft is made of 2014-t6 aluminum and is subjected to the distributed and concentrated torsional loadings shown where t=1. 7 kn⋅m.
Answer:
bbc
Step-by-step explanation:
If x # y = 2x + y, then 1 # 2 =
Answer:
1 # 2 = 4
Step-by-step explanation:
1 # 2 = 2*1 + 2 = 2 + 2 = 4
Put 62%, 0.71, 0.8, 5/8 in ascending order
Answer:
0.62 < 5/8 < 0.71 < 0.8
That’s it in ascending order
0.8 > 0.71 > 5/8 > 0.62
That’s it in descending order
Step-by-step explanation:
Answer:
62%, 5/8, 0.71, 0.8
Step-by-step explanation:
62% in form of a decimal is 0.62 and 5/8 is 0.625 when u round off its 0.63 which is 0.01 more than 62%. then 0.71 is 0.1 less than 0.8
The radius of a vegetable garden is 63m. If 1188m pf wire is given to fence around it, how many rounds of fencing can be made
Answer:
3 roundsStep-by-step explanation:
Circumference of the garden is:
C = 2πrC = 2*3.14*63 = 395.64 mNumber of rounds:
1188 / 395.64 = 3Radius=63m=r
Circumference
[tex]\\ \sf\longmapsto 2πr[/tex]
[tex]\\ \sf\longmapsto 2(3.14)(63)[/tex]
[tex]\\ \sf\longmapsto 6.28(63)[/tex]
[tex]\\ \sf\longmapsto 395.6m[/tex]
Wire=1188mRounds:-.
[tex]\\ \sf\longmapsto 1188/395\approx 3[/tex]
What is an equation of the line perpendicular to
y=1/5x+2 that contains (15,-4)
Answer:
y + 4 = -5(x - 15)
Step-by-step explanation:
The given line has a slope of 1/5. Any new line perpendicular to this given line has a slope which is the negative reciprocal of 1/5: -5.
Use the point-slope equation of a line: y - k = m(x - h), where (h, k) is the point through which the new line passes. Here h = 15 and k = -4, so we have:
y + 4 = -5(x - 15)
This line is perpendicular to the given line and also passes through (15, -4).
Theo leased a corvette for his wedding. The total cost (C) was $777. Find out how many hours the corvette was leased using the equation: C = 10h + 75
I MIGHT GIVE BRAINLY PLS HELP 100 POINTS
Answer:
70.2
Step-by-step explanation:
777 = 10h + 75
=> 702 = 10h
=> h = 70.2
Therefore, it took 70.2 hours to lease the corvette.
Hoped this helped.
Don’t understand please help
Answer:
Table I blank is 1
Table II blank is 1.398
to return a book to the library on time, Billy needs to read 40 pages every day. However, Billy reads 15 fewer pages than he should each day, and returns the book 6 days late. In how many days was he supposed to read the book?
Using proportions, it is found that he was supposed to read the book in 10 days.
This question can be solved by proportions, using a inverse rule of three, as when the number of pages read per day increases, the time to finish the book decreases.Reading 40 pages every day, he finishes the book in x days. He read 40 - 15 = 25 pages every day, and finished the book in x + 6 days, hence, the rule of three is:40 pages - x days
25 pages - x + 6 days
Applying line multiplication, as it is an inverse rule of three:
[tex]40x = 25(x + 6)[/tex]
[tex]40x = 25x + 150[/tex]
[tex]15x = 150[/tex]
[tex]x = \frac{150}{15}[/tex]
[tex]x = 10[/tex]
He was supposed to read the book in 10 days.
A similar problem is given at https://brainly.com/question/24372153
Who has the best conclusion?
A.Sheryl said the lowest grade was a 70 and the highest grade was a 92.
B.Shania said the highest grade was a 100.
C.Andrea said the lowest grade was a 68 and the highest grade was a 92.
D.Allen said the range of the scores was 32.
Answer:
B. Shania's conclusion is the only accurate one.
Step-by-step explanation:
Solve for x
#6:
X=_
#7
X= _
Step-by-step explanation:
for the first one let's write our equation
(13x+2)+(3x-4)+(5x-7)=180
Combine like terms
21x-9=180
Add 9 to both sides
21x=189
Divide both sides by 21
x=9
Now for the second one
Let's write our equation
(19x-18)+(7x+1)+(10x-9)=180
Combine like terms
36x-26=180
Add 26 to both sides
36x = 206
Divide both sides by 36
x = 5.72222...
: Mr. Burkett drove his car at an average speed of 70 miles per hour for 3.5 hours and then traveled at an
average speed of 65 miles per hour for 2.5 hours. What was the total distance in miles that he traveled during this time?
Answer:
Mr Burkett travelled 407.5 miles during his full trip.
Step-by-step explanation:
First, we must determine the distance he travelled in the first 3.5 hours. Luckily, we know his speed during that time so we can just multiply 70 miles per hour by 3.5 hours. That is 245 miles.
In the second step, we must determine the distance he travelled during the second part of his trip where he slowed down a bit. 65 miles per hour times 2.5 hours is 162.5 miles.
Finally, we can just add them! 245 + 162.5 = 407.5.
The times for running a 5K for a local charity event are Normally distributed with a mean time of 28 minutes and
standard deviation of 5.4 minutes. Which time represents the 60th percentile?
Find the z-table here.
A. 19.6 minutes
B. 26.6 minutes
C. 29.4 minutes
D. 36.4 minutes
Answer:
29.4 minutes represents the 60th percentile
Step-by-step explanation:
Given : The times for running a 5K for a local charity event are Normally distributed, with a mean time of 28 minutes and standard deviation of 5.4 minutes.
To Find : Which time represents the 60th percentile?
19.6 minutes
26.6 minutes
29.4 minutes
36.4 minutes
Solution:
time represents the 60th percentile
Means 60 % data = 0.6 below this
from z table , z score for this = 0.253
z score = ( Value - Mean ) / SD
=> 0.253 = ( Value - 28 ) /5.4
=> 1.3662 = Value - 28
=> Value = 29.3662
=> Value = 29.4
29.4 minutes represents the 60th percentile
6457/25 using partial products
Set up using the same way please.
Answer: 6457/25=258.28
Step-by-step explanation:
Answer:
258.28 Hope this helps! Please mark brainliest it means a lot to me
Step-by-step explanation:
Th=0
H=2
T=5
0=8
tenth=2
hundredth=8
You could get the answer by doing long division/standard algorithm
Definition: An event that is made up of two or more outcomes is called
Example: Rolling a 5 on a die and flipping heads on a coin.
785 to the nearest 10
How to graph an equation.
Answer:
Below
Step-by-step explanation:
To graph an equation, we must have a y-intercept and a slope. Now, our equation is y = mx + b
We just replace the slope with 'm' and the y-intercept with 'b'. Let's say that our slope is 4 and y-intercept is 5. Then our equation will be y = 4x + 5.
Hoped this helped.
solve pls brainliest
Answer:
0.92 can be written as a fraction, because it is a terminating decimal. ( See the following. )
[tex] \frac{23}{25} [/tex]
0.777... can't be wrtten as a fraction, because it is a repeating decimal.
0.444... can't be written as a fraction, because it is a repeating fraction.
0.5813.. can't be written as a fraction, because
it is a decimal that neither terminates nor repeats.
For example : Root numbers don't terminates or repeats.
[tex] \sqrt{ 2} = 1.41421...[/tex]
I hope it helps.
I NEED HELPP!!!
Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
_______________________________________________
Given all of this information, answer the following questions:
1. What is the original loan amount, i.e. how much were the total costs for tuition plus room & board for the four years that Penny attended the college?
2. What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)
3. Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)
I will mark most brainlest whoever gets it right for me :)))
Sorry I can't help you :(
If 6 numbers have a mean of 5, and five of the numbers are 3, 2, 1, 7, and 6, what is the sixth number?
Answer:
see below
Step-by-step explanation:
the total value of the 6 numbers is 30 and the sum of the given 5 numbers is 19 therefore the 6th number is 11
cost $ 99.99 Markup rate 10 %
!!!!!!!10 POINTS TO WHO EVER ANSWER I WILL BE GIVING MORE ON THE NEXT QUESTION!!!!!!!
Answer: %0.00100010001
Step-by-step explanation:
Here is an inequality -10+x÷4+5>7x-5÷3
Answer:
here is the answer x>1/2
Tim buys a book for $50.38. If he paid 3% in sales tax, then what did the book cost
before tax?
Answer:
Total cost of the book = $51.89
Step-by-step explanation:
Total cost of the book = Cost of the book + (cost of the book × sale tax %)
Total cost of the book = $50.38 + ($50.38 × .03) 3% = .03 as a decimal
Total cost of the book =$50.38 + $1.5114)
Total cost of the book = $51.8914
Total cost of the book = $51.89
10. Simplify each 12x°(x-4) x=6
Answer: 144
Step-by-step explanation:
since x=6 and im assuming ° means multiplication
12(6) times (6-4)
72 times 2
144
Answer:
144
Step-by-step explanation:
(12)(6)(6−4)
=144
someone please help
Step-by-step explanation:
polynomial identities means equations where the left and the right side are always identical (no matter what values we use for the variables).
so,
A is not.
(x + 2)³ = x³ + 8
(x+2)(x+2)(x+2) = x³ + 8
(x² + 4x + 4)(x+2) = x³ + 8
x³ + 4x² + 4x + 2x² + 8x + 8 = x³ + 8
x³ + 6x² + 10x + 8 is definitely not generally the same as x³ + 8
B is not.
x⁶ + x = (x-1)(x⁵ + x⁴ + x³ + x² + x)
x⁶ + x = x⁶ + x⁵ + x⁴ + x³ + x² - x⁵ - x⁴ - x³ - x² - x
x⁶ + x = x⁶ - x
that is definitely not generally equal.
C is an identity
(x² - 1)(x⁴ + x² + 1) = x⁶ - 1
x⁶ + x⁴ + x² - x⁴ - x² - 1 = x⁶ - 1
x⁶ - 1 = x⁶ - 1
yes, identical.
D is not.
(x+1)⁴ = x⁴ + x³ + x² + x + 1
(x+1)²(x+1)² = x⁴ + x³ + x² + x + 1
(x²+2x+1)² = x⁴ + x³ + x² + x + 1
x⁴ + 2x³ + x² + 2x³ + 4x² + 2x + x² + 2x + 1 =
x⁴ + 4x³ + 6x² + 4x + 1
that is definitely not generally the same as
x⁴ + x³ + x² + x + 1
E is an identity
(x+1)(x⁴ - x³ + x² - x + 1) = x⁵ + 1
x⁵ - x⁴ + x³ - x² + x + x⁴ - x³ + x² - x + 1 =
x⁵ + 1 = x⁵ + 1
yes, identical.
F is an identity
(x³-1)(x³+1) = x⁶ - 1
x⁶ + x³ - x³ - 1 = x⁶ - 1
x⁶ - 1 = x⁶ - 1
yes, identical.
You are choosing between two health clubs Club A offers membership for a fee of $21 plus a monthly fee of $20. Club B offers
membership for a fee of $35 plus a monthly fee of $13. After how many months will the total cost of each health club be the same?
Answer:
$$x=5$$, so after five months the costs would equal each other
Step-by-step explanation:
i think pls mark brainliest