All categories

2 years ago

Use row reduction to find the inverse of the given matrix if it exists, and check your answer by multiplication.

Mathematics

2 answers:

lakkis [162]2 years ago

8 0

Step-by-step explanation: see attachment below

Salsk061 [2.6K]2 years ago

7 0

Answer:

Step-by-step explanation:

Given the 2×2 matrix since the matrix consists of 2rows and 2columns, to find its inverse using row reduction method, we will augment the matrix given with a 2×2 identity matrix before carrying out the reduction on the resulting 2×4 matrices. The resulting matrix must be an identity matrix augmented with the inverse of the matrix in question. The process of reduction is as shown in simple steps.

[A | I] -> [I | A-¹] where

A is the given matrix

I is the 2×2 identity matrix

A-¹ is the inverse of the matrix

Check attachment for the reduced matrix.

You might be interested in

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than on

Kazeer [188]

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. Then, the probability of staying in the same state is 90%.

- For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. Then, the probability of staying in the same state is 80%.

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. Then, the probability of staying in the same state is 82%.

The transition matrix becomes:

$\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}$

The actual state matrix is

$\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right]$

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

$\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right]$

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

$\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right]$

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

$\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right]$

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

3 0

3 years ago

Which solution finds the value of x in the triangle below?

forsale [732]

I didn't get it can you post a picture with it too?

5 0

3 years ago

Read 2 more answers

Find the area of the shaded region.

skelet666 [1.2K]

Answer:

5x12

Step-by-step explanation:

easy math become i have iq of 12

also charli damelio is a horrible person becasue she let spoepel ethink vujvmvmvmvuvjvm i8vkvucjmcvucmcucvm

5 0

3 years ago

Y=4x+28 sorry some is cut off

Rus_ich [418]

Add
4
x
4
x
to both sides of the equation.
y
=
−
28
+
4
x
y
=
-
28
+
4
x
Rewrite in slope-intercept form.
Tap for more steps...
y
=
4
x
−
28
y
=
4
x
-
28
Use the slope-intercept form to find the slope and y-intercept.
Tap for more steps...
Slope:
4
4
y-intercept:
−
28
-
28
Any line can be graphed using two points. Select two
x
x
values, and plug them into the equation to find the corresponding
y
y
values.
Tap for more steps...
x
y
2
−
20
3
−
16
x y 2 -20 3 -16
Graph the line using the slope and the y-intercept, or the points.
Slope:
4
4
y-intercept:
−
28
-
28
x
y
2
−
20
3
−
16
x y 2 -20 3 -16
image of graph
y
−
4
x
=
−
2
8
y
-
4
x
=
-
2
8

28
x
28
x
28
x
2
28
x
2
28
x
3
28
x
3

7 0

3 years ago

What is the solution to the following equation? (4 points) 2(3x − 7) + 18 = 10

konstantin123 [22]

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*(3*x-7)+18-(10)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(2 • (3x - 7) + 18) - 10 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

6x - 6 = 6 • (x - 1)

Equation at the end of step 3 :

6 • (x - 1) = 0

Step 4 :

Equations which are never true :

4.1 Solve : 6 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2 Solve : x-1 = 0

Add 1 to both sides of the equation :

x = 1

One solution was found :

x = 1

7 0

3 years ago

Read 2 more answers