How do you find the inverse of a 3x3 matrix?

Answers

Answer 1

The inverse of a 3x3 matrix is found by creating an Adjugate Matrix.

How do you find the inverse of a 3x3 matrix?

Step 1 : For any matrix M find the adjoint matrix.

Finding the transpose of the cofactor matrix of a matrix M yields the adjoint of that matrix. Any 3x3 matrix element's cofactor is the determinant of the 2x2 matrix that results from deleting the element's row and column. While determining the cofactors, alternate + and - signs are also written.For example :

        [tex]\text{Let a matrix }M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]

                         [tex]M^{T}= \left[\begin{array}{ccc}1&0&5\\2&1&6\\3&4&0\end{array}\right][/tex]

                       Adj M = [tex]\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]

Step 2 :Find Determinant of a 3x3 Matrix

Find the sum of the product of the components of any row/column and their respective cofactors to determine the determinant of a 3x3 matrix.For example:

         [tex]M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]

       det (M)= 1 (0- 24 ) - 2 (0 - 20 )+3 (0- 5 )

                  = - 24 + 40 -15

                  = 40 - 39

                  = 1

         

Step 3 : Find inverse matrix [tex]M^{-1}[/tex]

M determinant can be  calculated in the first step to check that the inverse was possible. Now multiply each term in the matrix by that number. In each computation, replace the original term with the results. The outcome is the opposite of the initial matrix.

          [tex]M^{-1 } = \frac{1}{det (M)} (Adj M)[/tex]

For example :        

          [tex]M^{-1 } = \frac{1}{det (M)} (Adj M)\\\\M^{-1 } = \frac{1}{1}\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right]\\\\M^{-1 }=\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]

To learn more about matrix, refer:

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Related Questions

Hurry please! 30 points!

A ladder rests against the side of a barn. The tip of the ladder reaches 20 feet up the wall and the base of the ladder reaches a point on the ground 12 feet from the wall. About how tall is the ladder?

A. 23 ft
B. 16 ft
C. 12 ft
D. 9 ft

Answers

Answer:

A - 23ft

Step-by-step explanation:

Pythagorean theorem: 12^2 + 20^2 = X^2.

X^2 = 544. X = sqrt(544) which is around 23ft

slope: -1 intercept: -7.9

what is the slope of each line that passes through the points?

what is the answer

Answers

Answer:

-1

Step-by-step explanation:

Since the question LITERALLY stated the slope is -1, the slope is literally -1

1.) find the first four terms in ascending powers of X in the expansion (2+2X)¹² .show your working!!​

Answers

Answer:

15/8

Step-by-step explanation:

Which expression is not equal to 1?

sin θ csc θ
cos θ sec θ
tan θ cot θ
sin θ cos θ

Answers

Answer:

sin θcos θ

hope it is helpful to you

Answer:

sin A cos A

Step-by-step explanation:

[ I don't know to type angle theta here so assume A as theta]

As , sin A= p/ h

cos A= b/ h

so,

sinA cosA = p/ h × b/h

= pb/ h^2 ( which is not equal to 1 )

Tip; you can easily verify other relations expressing trigonometric ratios in terms of p,b & h and further simplifying..

PLEASE HELP WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST

Answers

The answer is d i can explain if you want or need

Caleb earns points on his credit card that he uses toward future puchases. He earns four points per dollar spent on flights, two points per dollar spent at hotels,and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 more than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

Answers

Answer:

Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases.

Step-by-step explanation:

It costs $15,700 to build a particular car. This car sells for $24,322. What is the percent markup on the car to the nearest percent.

Answers

Answer: $15,700 - $24,322= 8622

Step-by-step explanation:

All you have to do is subtract

Simplify the expression: 4(x + 3) = 40

Answers

Answer:

x=7

Step-by-step explanation:

4x+12=40

-12

4x=28/4

Answer:

x =7

Step-by-step explanation:

4x + 12 = 40

4x + 12 - 12= 40 -12

4x = 28

4/4= 28/4

x= 7

6x+?= 10x

6x−?= 2x

6x+?= 2x

6x−?= 10x

6x+?=- 10x

6x−?= x

6x+?= 0

6x−?= 6

6x+?= 10

6x−?= 4x - 10

Answers

Answer:

x=0

Step-by-step explanation:

Let's solve your equation step-by-step.

6x+x=10x

Step 1: Simplify both sides of the equation.

6x+x=10x

(6x+x)=10x(Combine Like Terms)

7x=10x

7x=10x

Step 2: Subtract 10x from both sides.

7x−10x=10x−10x

−3x=0

Step 3: Divide both sides by -3.

−3x/−3 = 0/−3

x=0

Now you can figure out which one is the best solution

Answer would be x=0
Hope you have a great day

Mr. Henry spent $15 on a new hat this week. He learned that the same hat available on
sale at $12 last week. What was the percentage increase in the price of the hat this
week?

Answers

Last week was $12
This week is $15
%increase = (15-12)/12 = 25%

Please help me with this homework

Answers

Answer:

20

Step-by-step explanation:

use pythagorean theorem:

[tex]12^{2}[/tex] + [tex]16^{2}[/tex] = [tex]c^{2}[/tex]

144 + 256 = [tex]c^{2}[/tex]

400 = [tex]c^{2}[/tex]

[tex]\sqrt[ ]{400}[/tex] = c

20 = c

HELP OMG
I LOST MY AIRPODS AT SCHOOL

Answers

Answer:

how should we help?

Step-by-step explanation:

Answer:

dang that sucks..... try and play music at max vol and see if you hear any music coming from anywhere that's probably were the airpods are, if they are in the case then i dont know if u would hear anything. It all depends...

~ i hope this has helped ya out some how, hope ya find your airpods my friend!~

Step-by-step explanation:

please help !
A local paintball facility charges $30 to play plus $0.25 per paintball pellet used. Elijah plans on playing paintball and has $60 to spend at the facility. Which equation can be used to determine p, the number of paintball pellets he can use if he spends exactly $60?

A. 30 + 0.25p = 60
B. 30 + 0.25 = 60p
C. 30p + 0.25 = 60
D. 30 − 0.25p = 60

Answers

Step-by-step explanation:

Hello! I believe the answer is A. 30+0.25p=60.

Elijah has to pay a facility charge which is 30$. So we can go ahead and write that down! He has 60$ to spend, but he has to pay $0.25 per paintball. So we write that as 30+0.25p=60!! If you have any questions comment doen below!

Answer:i think it A to

Step-by-step explanation: it is the only one correct

HELP ME FOR 5 AND 6 PLEASEEEEE HDJSHSHS

Answers

Answer:

For number five your answer would be C and for number 6 it would be C

Step-by-step explanation:

you take 12 and multiply by 9 which gives you 108

5. B
6. C.
I don’t know how to explain the situation. It is really hard to explain on text.

Pls Help Asap pls T^T

Answers

Answer: think its c

Step-by-step explanation:

I believe the answer is 18%

Solve for angle B, then side a. Round to the nearest tenth.

Answers

Answer:

Angle B: 28 degrees

Side a: 27.6

Step-by-step explanation:

Angle B:

180-112-40=28

Side a:

sin 28/14 = sin 112/a

a = sin 112(14)/sin 28

a = 27.6

what is the measure of each exterior angle of a regular 67-gon?

Answers

360/67. Like 5.37. ...............

The measure of  each exterior angle of a regular 67-gon is 5.73

Given that,

There is the regular 67-gon.And, the sum of exterior angle is 360.

Based on the above information, the calculation is as follows:

[tex]= 360\div 67[/tex]

= 5.73

Learn more: brainly.com/question/17429689

In the following triangle, angle A measures 49° and angle C measures
62.

Answers

Answer:

The measure of angle B is 69°.

Step-by-step explanation:

All angles of the triangle should add up to 180°, so you add angle A and angle C together, and then subtract that number from 180.

49 + 62 = 111

180 - 111 = 69

69°

Please help im lost..

Answers

Answer:

c

Step-by-step explanation:

SCENARIO A:When the Puertas family moved into their home 14 yearsago, there was alemon and orange tree in their backyard. Both treeshave since been growing ata constant rate. 2 years after the Puertas familymoved in, the lemon tree was 7feet tall, and 8 years after they moved in, the lemontree was 10 feet tall. As forthe orange tree, 3 years after the Puertas familymoved in, it was 4 feet tall, and7 years after they moved in, the orange tree was 8feet tall.Question 1:How many years afterthe Puertas family moved in willthe lemon tree and theorange tree be the same height?What height will theybe?

Answers

Answer: 18

Step-by-step explanation:

Simplify.
27²=
FAST plsssssssssssssssssssssss

Answers

Answer:

729

Step-by-step explanation:

27²=  (27)(27)=729

Choose a positive number. Using this number as
the base, evaluate it when the exponent is 3,0,
and -2. Show all work.

Answers

Answer:

Step-by-step explanation:

Choose 3.

3^3 = 27;

3^0 = 1; and

3^(-2) = 1/9

Need ASAP please help

Answers

Answer:

POSSIBLY 1

Step-by-step explanation:

A 10 ft. tree casts a 14 ft. shadow. If a building casts a 280 ft. shadow, how tall is the building?

Answers

Answer: The building is 200ft tall

Explanation: if you Set up a ratio.
10 is to 14 as x is to 280.

Find the area of the largest square contained by a circle of radius r = 1cm. Explain your answer and justify that it is correct. Hint: Use the pythagorean theorem.

Answers

Answer:

2 square cm

Step-by-step explanation:

Given :

A square is inscribed in a circle whose radius is r = 1 cm

Therefore, the diameter of the circle is 2 r = 2 x 1

                                                                      = 2 cm.

So the diagonal of the square is 2r.

Using the Pythagoras theorem, we find each of the side of the triangle is [tex]$r \sqrt 2$[/tex].

Therefore, the area of the square is given by [tex]$\text{(side)}^2$[/tex]

                                                                         = [tex]$(r\sqrt 2)^2$[/tex]

                                                                         [tex]$= 2 r^2$[/tex]

                                                                         [tex]$= 2 (1)^2$[/tex]

                                                                         [tex]$=2 \ cm^2$[/tex]

Hence the area of the largest square that is contained by a circle of radius 1 cm is 2 cm square.

Help please!!!
Find the value of x. If necessary, write your answer in simplest radical form.
24
20

Answers

Answer: 46 is your answer hope this helped

Step-by-step explanation:

Answer:

[tex]4 \sqrt{11} [/tex]

Step-by-step explanation:

According to Pythagoras Theorem,

[tex] {(hypotenuse)}^{2} - {height}^{2} = {(base)}^{2} [/tex]

[tex] = > {24}^{2} - {20}^{2} = {x}^{2} [/tex]

[tex] = > \: {x}^{2} = 576 - 400[/tex]

[tex] = > {x}^{2} = 176[/tex]

[tex] = > x = \sqrt{176} [/tex]

[tex] = > x = \sqrt{2 \times 2 \times 2 \times 2 \times 11} [/tex]

[tex] = > x = 2 \times 2 \sqrt{11} [/tex]

[tex] = > x = 4 \sqrt{11} (ans)[/tex]

Solve for x. Show all your steps/work.
(¼)x + 1 = 22x

Answers

22x-1/4x= 1
21.75x=1
x=0.046

Im not sure tho:) but probably its correct
Answer is x= 4/87
Step 1: multiply 4 by both sides of the equation which is 22. Which gives you x+4= 88x
Step 2: Move the constant to the right-hand side and change its sign (it was +4 but it’s now -4) then move the variable to the left-hand side and change its sign (which is +88 but is now -88x)
Step 3: collect like terms which is 1-88x that gives you -87x= -4
Step 4: divide both sides by -87
That gives you the answer

1/4x +1= 22
Multiply by 4
X+4 = 88x
Move the terms
X- 88x= -4
Collect like terms
-87x=-4
Divide by -87
Equals 4/87

what is the volume of this pyramid?

the options are
A. 720
B. 1080
C. 1440
D. 2160

Answers

the answer is C grrrr

PLZS HELP THIS IS MY LAST QUESTION!!

Answers

Answer:

x = 30

Step-by-step explanation:

According to figure,

54° + 3x+36° = 180° [Linear pair]

=> 3x + 90 = 180

=> 3x = 180 - 90

=> 3x = 90

[tex] = > x = \frac{90}{3} [/tex]

=> x = 30 (Ans)

Answer:

x=30

Step-by-step explanation:

cuz that line is 180 degrees and using algebra you can subtract 54 from both sides and get 126 then u have to subtract the 36 from both side to geth 90 and then divide the 3x to get x by itself which would leave u with 30 so x=30

Mikel gave a $1.32 tip for an order that cost $8.80.
Determine whether or not each tip below is proportional to Mikel's tip.
Proportional to Mikel's tip
Not proportional to Mikel's tip
$2.22 tip for a $14.80 order
$1.86 tip for a $10.50 order
ООО
$0.78 tip for a $5.20 order

Answers

Answer:

Step-by-step explanation:

Multiple the numbers one by one and the answers you’ll get u can choose to divide multiple plus or minus and u will get the answer

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