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MakcuM [25]
2 years ago
7

Show that ifAB=IandAC=I, then it follows that B=C. Explain how this proves thatthe inverse of the matrix A is unique.

Mathematics
1 answer:
Anna007 [38]2 years ago
6 0

Answer with Step-by-step explanation:

Suppose that a matrix has two inverses B and C

It is given that AB=I and AC=I

We have to prove that Inverse of matrix is unique

It means B=C

We know that

B=BI where I is identity matrix of any order in which number of rows is equal to number of columns of matrix B.

B=B(AC)

B=(BA)C

Using associative property of matrix

A (BC)=(AB)C

B=IC

Using BA=I

We know that C=IC

Therefore, B=C

Hence, Matrix A has unique inverse .

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Trevor has two fraction models, each divided into equal-sized sections. The
erma4kov [3.2K]

Answer:

I will answer in a general way because the options are not given.

We know that the area of model A is smaller than the area of model B.

For model A, we have 72 shaded sections, out of 100.

Then the quotient of model A is:

72/100 = 0.72

For model B we have 10 sections, and x shaded ones.

Because model B is greater than model A, we know that:

x/10 should be larger than 72/100

then we have the inequality:

x/10 > 0.72

x > 0.72*10

x > 7.2

And we can not have more than 10 shaded sections (because there is a total of 10 sections) then:

10 ≥ x > 7.2

Then x can be any whole number in that interval.

the possible values of x are:

x = 8

x = 9

x = 10

5 0
2 years ago
When a force of 30 N acts on a certain object the acceleration of the object is 5m/s2 if the force is changed to 54 N what will
PtichkaEL [24]

Answer:

The correct answer is 9 m per second^{2}

Step-by-step explanation:

Force is defined by mass of an object times it's acceleration.

Let the mass of the object be m kilograms.

When a force of 30 N acts on a certain object the acceleration of the object is 5 m per second^{2}

∴ 30 = m × 5

⇒ m = 6.

If the force is changed to 54 N, let the acceleration of the object be x  m per second^{2}.

∴ 54 = m × x

⇒ x = \frac{54}{6} = 9

Thus when the force is 54 N, the acceleration of the object is 9 m per second^{2}.

6 0
3 years ago
10. Dan picks 18 baskets of apples
Paladinen [302]

Answer:

1 basket = 24 apples

24 × 18 = 432 apples

(use cross multiplication method)

1 apple = 15 cents

432 = x

\frac{1x}{1}  = 6.480

x = 6.480 cents

7 0
2 years ago
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where
kipiarov [429]

Answer:

<h2>a) 0.5367feet</h2><h2>b) 0.5223feet</h2><h2>c) 0.7292feet</h2>

Step-by-step explanation:

Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).

The amount of growth can be gotten by integrating the given rate equation as shown;

\int\limits {0.5 + \frac{6}{(t+4)^{3} }  } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} }  } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \  where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C

a)  The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from  t =1 to t = 2

\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} }  } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\   = 0.9167 - 0.5 + 0.12\\= 0.5367feet

b)  The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from  t =2 to t = 3

\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} }  } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\  = 1.439 - 0.9167\\= 0.5223feet

c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown

\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} }  } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\   = 0.9167 - 0.1875\\= 0.7292feet

8 0
2 years ago
-3/4 to the third power
Mkey [24]
(-\frac{3}{4})^3=-\frac{3^3}{4^3}=-\frac{27}{64}=-0.421875\approx0.4
4 0
3 years ago
Read 2 more answers
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