1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
barxatty [35]
3 years ago
14

Find the inverse of the following matrix without using a calculator 1-1 2 -3 2 1 0 4 - 25

Mathematics
1 answer:
Artist 52 [7]3 years ago
4 0

Answer:

18  -(17/3)   (5/3)

25  (25/3)  (7/3)

4    (4/3)     (1/3)

Step-by-step explanation:

You can solve this problem by using the Gauss-Jordan method.

You have the original matrix and then the Identity matrix.

So:

Original              Identity

1 -1 2                    1 0 0

-3 2 1                   0 1 0

0 4 -25                0 0 1

By the Gauss-Jordan method, in the original place you will have the identity and in the place that the identity currently is you will have the inverse matrix:

So, let's start by setting the first row element to 0 in the second and the third line.

The first row element of the third line is already at zero, so no changes there. In the second line, we need to do:

L2 = L2 + 3L1

So now we have the following matrixes.

1 -1 2        |            1 0 0

0 -1 7       |            3 1 0        

0  4 -25   |            0 0 1

Now we need the element in the second line, second row to be 1. So we do:

L2 = -L2

1 -1 2        |            1 0 0

0 1 -7       |            -3 -1 0        

0  4 -25   |            0 0 1

Now, in the second row, we need to make the elements at the first and third line being zero. So, we have the following operations:

L1 = L1 + L2

L3 = L3 - 4L2

Now our matrixes are:

1 0 -5       |            -2 -1 0

0 1 -7       |            -3 -1 0        

0 0 3       |            12 4 1

Now we need the element in the third line, third row being one. So we do:

L3 = -L3

1 0 -5       |            -2  -1     0

0 1 -7       |            -3  -1      0        

0 0 1       |            4    (4/3) (1/3)

Now, in the third row, we need the elements in the first and second line being zero. So we do:

L1 = L1 + 5L3

L2 = L2 + 7L3

So we have:

1 0 0 |       18  -(17/3)   (5/3)

0 1 0 |       25  (25/3)  (7/3)

0 0 1 |       4    (4/3)     (1/3)

So the inverse matrix is:

18  -(17/3)   (5/3)

25  (25/3)  (7/3)

4    (4/3)     (1/3)

You might be interested in
Can someone tell me whats1+1​
Andreyy89

Answer:

2

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A Rhombus with diagonal 1 equal to 5 ft and diagonal 2 equal to 8 ft
Minchanka [31]

Answer:

Area = 20 ft²

Step-by-step explanation:

Area of a thrombus

½ × d1 × d2

½ × 5 × 8

20

4 0
3 years ago
Read 2 more answers
2(x + 4) + 2x + 3 = 3x + 16<br>what does x eqaul​
Ad libitum [116K]

Answer:

x=5

Step-by-step explanation:

2(x+4)+2x+3=3x+16

One solution was found :

                  x = 5

7 0
3 years ago
Read 2 more answers
Shawn incorrectly graphed the inequality -x-2y≥8 as shown below Explain shawn mistake ​rotate phone if u need to
Aleks04 [339]

Answer:

He failed to flip the inequality

y ≤-1/2x-4

Step-by-step explanation:

-x-2y ≥8

Add x to each side

-x+x-2y ≥x+8

-2y ≥x+8

Divide by -2.  Remember to flip the inequality

-2y/-2 ≤-1/2 x +8/-2

y ≤-1/2x-4

Shawn shaded the wrong side of the line.

Y is less than or equal to .  He failed to flip the inequality

3 0
3 years ago
Is 1/2 equivalent to 5/8
kompoz [17]
<span>No. 

To check this yourself, you need the denominators to be the same to be able to easily compare the two. 

For example, does 5/8 = 40/64? 

1. Determine what you would need to do to the denominator in 5/8 to make it 64. (Multiply it by 8) 
2. Find what fraction is equal to 1 with a denominator of 8. (8/8) 
3. Multiply the fraction 5/8 by the one you just found (8/8), numerator times numerator, denominator times denominator. 
4. Compare the answer with the second fraction. 

It is important that when you multiply the denominator by any number you multiply the numerator by the same number. This is to preserve the fraction's value. This works because any number divided by itself is equal to 1, AND when you multiply any number by 1 (whether 1 is in the form of 1 or 4/4 or 8/8 or 234/234), the answer is always equal to the original number. 

Another way to check would be to simply enter 1/2 into a calculator, write down the answer. Next enter 5/8 into a calculator. If the answers are the same, they are equal.</span><span>
</span>
8 0
2 years ago
Read 2 more answers
Other questions:
  • Subtract.<br> −1 1/3 − 1/6
    8·2 answers
  • Which expression is equivalent to 6(8-n)-8
    6·1 answer
  • I need help. 2/7 of _ is 14?
    7·1 answer
  • The southward translation of the rose garden is along which axis? What integer represents a change of four yards south?
    6·1 answer
  • AP CAL AB HELP!
    6·1 answer
  • Gary mails the third power of 10 flyers in one week.How many fliers does gary mail
    8·1 answer
  • Given f(x)=2x^2 8 and g(x)=5x-6, find each function.(f g)(x)(f*g)(x)
    11·1 answer
  • Please help I need a better grade in this class.
    11·1 answer
  • Please help me with this its getting late and im almost done
    13·1 answer
  • What is the solution to the system x + y = 5 and 3x - y = 3?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!