Find an equation for this line?

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]

Answer:

P = 34 1/8 inches

Step-by-step explanation:

P = 2l + 2w

P = 2(10 3/16) + 2(6 7/8)

convert 10 3/16 to an improper fraction:  163/16

convert 6 7/8 to an improper fraction:  55/8, which equals 110/16

P = 2(163/16) · 2(110/16)

P = 326/16 + 220/16

P = 546/16

P = 34 1/8 inches

Answer:

No, because if you do the vertical line test, the line will hit that two times, Therefore it is not a function.

Step-by-step explanation:

Answer: at least 2

Step-by-step explanation: idek

Answer:

-3/2

Step-by-step explanation:

The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

Let x represent the number of Pi Day T-shirts sold.

They are selling Pi Day T-shirts for $7.50 each, So to raise $500:

7.5x > 500

Dividing through by 7.5:

7.5x / 7.5 > 500 / 7.5

x > 66.7

Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

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Answer:

The given equation is true for all x.

Step-by-step explanation:

Answer: 21120 feet.

Step-by-step explanation: We start with the fraction 1/180, found by putting 20 seconds over one hour. Then, we need to get the amount of miles the speed of sound travels in 20 seconds. We can use the fraction above as a ratio to get it. 720/1 x 1/180 = 4 miles. Then, we'll just do 4 times 5280, which is 21120.

The distance travelled by sound in 20 seconds is 21120 feet.

In unit time the distance covered by any object is called speed.

In mathematical term, Speed is express as S=D/T,

where S=speed, D=distance, T= time.

Given that,

The speed of sound = 720 miles per hour.

According to given condition,

1 hour = 720 miles

Since, 1 hour = 60 minutes

60 minutes = 720 miles

1 minute = 12 miles.

1 minute = 60 seconds

60 second = 12 miles

1 second = 12 / 60  = 1/5 miles

20 second = 20 / 5 = 4 miles

According to given condition,

1 mile = 5280 feet

Therefore,

20 second = 5280 x 4 = 21120 feet

The distance travelled in 20 seconds is 21120 feet.

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Answer:

125 square tiles

Step-by-step explanation:

(800*10)/8^2=8000/64=125

Answer:

See Below

Step-by-step explanation:

I think you mean 2 the the fourth power, showing 2, with an exponent of 4.

To calculate this, you multiply your base, 2, by itself as many times as the exponent states. Like, 2x2x2x2 because you are multiplying it 4 times by 2.

2x2=4, then 4x2=8, then 8x2= 16.

Hope this helps!

Answer:

20

Step-by-step explanation:

first, find out how much money you already made:

78 x 3 = 234

then, find out how much more you need to make:

350-234=116

divide the price of candy baskets by the amount of money left y out need to make:

116/6=19.3

round becauee you can’t sell .3 of a basket

19.3 rounds to 20

Answer:

[tex]y=\frac{1}{2} x+4[/tex]

Step-by-step explanation:

so the last option

hope this helps!

Answer:

It should be A & D

Step-by-step explanation:

These two are the only ones that have the exact same numbers on all three sides. They are congruent based on SSS.

7 1/2.

2 goes into 15 7 times with one left over.

Answer:

y = 5

Step-by-step explanation:

first you subtract 5y from itself and from 7y

then you'll get: 2y + 2 < 12

then subtract the 2 from itself and from the 12

that will give you: 2y < 10

then just divide the 2 from itself and that eliminates the 2 but keeps the y, and divide the 10 by the 2

that'll give you y = 5

Answer:

y = 13x

Step-by-step explanation:

Substitute 2 in x and you'll get 26:

y = 13•2

y = 26

Answer: 12

Step-by-step explanation:

180 = 76 + (3x+3) + (6x-7) = 12

Answer:

4x

Step-by-step explanation:

Simply add 4 and x, and that is 4x.

Answer: 31.6

Step-by-step explanation:

Answer:

≈ 31.7 yd

Step-by-step explanation:

let the missing side be x , then using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 9² = 33²

x² + 81 = 1089 ( subtract 81 from both sides )

x² = 1008 ( take square root of both sides )

x = [tex]\sqrt{1008}[/tex] ≈ 31.7 yd ( to the nearest tenth )

Jill will have taken 21 in 65 days because 65 divided by 3 is 21.6666666667.

Joe will have taken 16 in 65 days because 65 divided by 4 is 16.25.

Answer/Step-by-step explanation:

To Find the best price divided each

Kroger → 1.52/4=0.38

Publix → 175/5=35

Ingles → 1.02/3=0.34

Walmart → 2.46/6=0.41

Base on the data we can tell that Ingles have the best price.

Answer:

2/3

Step-by-step explanation:

4 cats / 6 dogs  = 2/3

simplify by dividing by 2

Answer:

J

Step-by-step explanation:

Answer:

(x+3)(x+5)(x-2)(x-1)(x^2+2x+4)(x^2+x+1) where the given one is bolded the 2 binomials is italicized  and the 2 trinomials is underlined

Step-by-step explanation:

3/8 + 34/16

15/6 can be simplified to 2 1/2

The answer for 3/8 + 34/16 can be simplified to 2 1/2

Answer:

25

Step-by-step explanation:

Because when you add all the cost and divide by the amount of tickets you get 25