Answer:
true
Step-by-step explanation:
How to find left and right inverse of a 3x2 matrix.
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]
y = 3x + 21. which ordered pair is a solution to the equation
Answer:
(1, 24 )
Step-by-step explanation:
Substitute any value of x into the equation and evaluate for y
x = 1 → y = 3(1) + 21 = 3 + 21 = 24 , then
(1, 24 ) is a a solution to the equation
given f(x)=2x^3+kx-9 and x-1is a factor of f(x), then what is the value of k?
When it says the "x - 1 " is the factor of that function means when you find the root of the phrase x - 1 which is x = 1 , put it in the function then you have to get zero for the answer :
thus :
[tex]f(1) = 0[/tex]
Thus :
[tex]2 \times {1}^{3} + k(1) - 9 = 0[/tex]
So :
[tex]2 + k - 9 = 0[/tex]
[tex]k - 7 = 0[/tex]
Add both sides 7
[tex]k - 7 + 7 = 0 + 7[/tex]
[tex]k = 7[/tex]
There you go...
Have a great day ❤
on weekends a movie ticket costs $10.50. form an inequality and solve it to find the maximum number of tickets kate can buy with $205
STEP BY STEP EXPLANATION PLEASE
$10.50
10 Tickets would be $105.00
$105.00 - $10.50 = $94.50 so 9 Tickets would be $94.50
$105.00 + $94.50 = $199.50
$205.00 - $199.50 = $5.50 which isn't enough for another ticket.
10 Tickets + 9 Tickets = 19 Tickets.
I need help quick desperate
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
The last time it placed an order for ingredients, Sweet Treats Bakery ordered 7,160 kilograms of sugar. This time, the bakery is ordering 40% less sugar. How much sugar is that?
Answer:
4296 kg
Step-by-step explanation:
40/100 = x/7160
716 times 6 is 4296
4-7 questions need help
Name two pairs of congruent angles using the figure shown.
Option 1: ∠JKM ≅ ∠KJL and ∠JLM ≅ ∠KML
Option 2: ∠JLM ≅ ∠KJL and ∠JKM ≅ ∠KML
Option 3: ∠JKM ≅ ∠JLM and ∠KJL ≅ ∠KML
Option 4: ∠JLM ≅ ∠KJL and ∠JLM ≅ ∠JKM
the ratio 18:24 in its simplest form is?
Answer:
3:4
Step-by-step explanation:
18 = 2 * 3 * 3
24 = 2 * 2 * 2 * 3
HCF = 2 * 3 = 6
Divide by 6
18: 24 = 18÷6 : 24÷6
= 3 : 4
Answer:
it's 3:4
Step-by-step explanation:
18 ÷ 6 : 24 ÷ 6
3 : 24 ÷ 6
=3:4
YES I WILL MARK BRAINLIST :
Find the 11th term if a8=8 and a20=44.
your internet provider offers two different plans. One plan costs $.02 per email plus a $9 monthly service charge. the other plan costs $.05 per email with no service charge.
Answer:
Step-by-step explanation:
y=.02x+9 - First Part
y=.05x - Second Part
If 5 gallons of gas cost $7.79, how much
will 7 gallons cost?
Answer:
$10.91
Step-by-step explanation:
7 gallons cost:
[tex](\frac{7.79}5}) (7)=\frac{(7.79)(7)}{5} =10.906[/tex]
rounded to cents: 10.91
I hope this help you
please please help! Ill give brainliest
worded problem image attached
6. Order the following decimal numbers
from least to greatest.
0.3
3.45
34.5
1.03
Answer:
In order: 0.3 - 1.03 - 3.45 - 34.5
Step-by-step explanation:
0.3 is less than 1. 1.03 is over 1. 3.45 is over 3. 34.5 is over 34, which is the greatest.
What is the value of x?
A hexagon (6 sides)
133°
112°
x°
120°
128°
100°
please help asap, no links
Answer:
X is 120° I hope this helps you
Isosceles trapezoid ABCD has legs AB and CD, and base BC. If AB = 3y - 4, BC = 2y -3, and CD = 4y - 18, find the value of y.
Answer:
(6)
Step-by-step explanation:
Since it is an isosceles trapezoid the length of the two legs (i.e. AB = 5y-10 and CD = 2y+8) are equal. In other words,
5y - 10 = 2 y + 8
Subtract 2y from each side:
5y - 2y - 10 = 8
Now add 10 to each side
5y - 2y - 10 + 10 = 8 + 10 =>
3y + 0 = 18 =>
3y = 18 =>
y = 6
REWARDING BRAINLIEST!
What is the value of x?
Enter your answer in the box.
x =
Answer:
7
Step-by-step explanation:
5/45 = 3/2x+13
Blair's average on the first five in-class tests is 67. If this is not pulled up to at least a 70,
Blair will not be allowed to watch any more of their favorite Netflix shows. To avoid
losing those access privileges, what is the lowest score Blair can afford to earn on the last
in-class test? Assume that all tests carry equal weight.
Answer:
85
Step-by-step explanation:
x/5 = 67
x=335
(x+y)/6 = 70
(335+y)/6 = 70
335+y=420
y=85
Answer:
85
Step-by-step explanation:
Average is calculated as
average = [tex]\frac{sum}{count}[/tex]
Here
[tex]\frac{sum}{5}[/tex] = 67 ( multiply both sides by 5 )
sum = 335
let x be the mark required to raise average to 70 , then
[tex]\frac{335+x}{6}[/tex] = 70 ( multiply both sides by 6 )
335 + x = 420 ( subtract 335 from both sides )
x = 85
Blair must score at least 85 on his last test
The maximum land speed of a cheetah is about 120km/hour.
What is this speed limit, rounded to the nearest whole number, in m/s?
Answer:
33 m/s
Step-by-step explanation:
120 km/h × (1 h)/(3600 s) × (1000 m)/(1 km) ≈ 33 m/s
_____
Additional comment
In general, units conversion is done by multiplying by a factor whose numerator and denominator have equal values, but different units. The units in that fraction need to be arranged to cancel the units you don't want and leave the units you do want.
write answer in scientific notation. (2.66×10¹³)÷(9.5×10⁵)
Answer: 28,000,000
Step-by-step explanation:
This is a long one.
Start with (1) 2.66 times 10 to the 13th = 26,600,000,000,000 {2.66E13}
(2) 9.5 times 10 to the 5th = 950,000
(3) 2.66E13 divided by 950,000 = 28,000,000
If this dosnt make any sense dont hesitate to say so.
Find the length of side x to the nearest tenth.
309
X
60°
Please help me fast I am in the middle of a test and I will give a brainleist.
Answer:
okay I believe it's A sorry If I'm wrong
Step-by-step explanation:
Answer:
St^{23}\sec \left(o\right)ndsago+5pts^6c-5b+18.2-2b+c+3
ep-by-step explanation:
Factor out the GCF from the terms of the polynomial –4y^5 + 6y^3 + 8y^2 – 2y.
I know that it is either B or D but I got confused
Answer:
D
Step-by-step explanation:
Here’s the full picture only 44, 45, 46, and 47
Answer:
m∠6 = 115; m∠5 = 115; m∠1 = 130; m∠4 = 65
Step-by-step explanation:
44. m∠6 = 180 - 65 = 115
45. m∠5 = 180 - 65 =115
46. m∠1 = 180 - 50 = 130
47. m∠4 = 180 - (50+65) = 180 - 115 = 65
Answer:
the person below is correct
Step-by-step explanation:
hope it helped have an amazing night :)❤
(PICTURE PROVIDED)
HELPPPPPPP PLS
A: 5/4
B: 3/2
C: 6/5
D: 2/3
Answer:
I think its 6/5 or 2/3
Step-by-step explanation:
Answer:
1. A
2. C
3. D
4. C
5. D
Step-by-step explanation:
You're welcome
Imagine that you have been asked to write a letter to a 7thgrader. Using academic vocabulary and 5-7 complete sentences, write a letter teaching a 7thgrader about something you have learned in 8thgrade Math this year.
please help me!
Answer:
step 1: what have you learned?
We cant help you because we do not know what you have learned.
but if you comment your vocab words and what u learned i can help you
Step-by-step explanation:
Use intercepts to graph the equation -x+5y=5
Kayden practices the piano 609 minutes in 3 weeks. If t represents the total time he
practices for any number of days, d, write a proportional equation for t in terms of d
that matches the context.
Answer:
Step-by-step explanation:
For a school fund raising project, Aiden and Jacob collected money in the ratio 3.5;6.8. Jacob collected $115.50 more than Aiden. Find the total amount of money they collected
Answer:
Step-by-step explanation:
A. Complete the table if y varies
directly as x or x2
B. Complete the table if y varies inversely as x.
Direct variation is represented by the equation y = k × x and inverse variation is represented by y = k/x
Table 1:
y = k × x
30 = k × 5
30 = 5k
k = 30/5
k = 6
So,
y = 30
y = 30 k = 6
y = 30 k = 6x = 5
y = 30 k = 6x = 5Equation: y = 6x
y = k × x
y = 10 × 8
y = 80
So,
y = 80
y = 80 k = 10
y = 80 k = 10x = 8
y = 80 k = 10x = 8Equation: y = 10x
y = 3x
18 = 3x
x = 18/3
x = 6
So,
y = 18
y = 18k = 3
y = 18k = 3x = 6
y = 18k = 3x = 6Equation: y = 3x
y = 2x²
72 = 2x²
x² = 72/2
x² = 36
x = √36
x = 6
So,
y = 72
y = 72k = 2
y = 72k = 2x = 6
y = 72k = 2x = 6Equation: y = 2x²
Table 2:
y = k/x
5 = k/6
5 × 6 = k
30 = k
So,
y = 5
y = 5k = 30
y = 5k = 30x = 6
y = 5k = 30x = 6Equation: y = 30/x
y = k/x
y = 36/4
y = 9
So,
y = 9
y = 9k = 36
y = 9k = 36x = 4
y = 9k = 36x = 4Equation: y = 36/x
y = 60/x
20 = 60/x
20x = 60
x = 60/20
x = 3
So,
y = 20
y = 20k = 60
y = 20k = 60x = 3
y = 20k = 60x = 3Equation: y = 60/x
y = 24/x
y = 24/12
y = 2
So,
y = 2
y = 2k = 24
y = 2k = 24x = 12
y = 2k = 24x = 12Equation: y = 24/x
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