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]
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In the following triangle, angle A measures 49° and angle C measures
62.
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°
Which expression is not equal to 1?
sin θ csc θ
cos θ sec θ
tan θ cot θ
sin θ cos θ
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..
A 10 ft. tree casts a 14 ft. shadow. If a building casts a 280 ft. shadow, how tall is the building?
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 $60?
A. 30 + 0.25p = 60
B. 30 + 0.25 = 60p
C. 30p + 0.25 = 60
D. 30 − 0.25p = 60
Step-by-step explanation:
Hello! I believe the answer is A. 30+0.25p=60.
Elijah has to pay a facility charge which is 30$. 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
PLEASE HELP WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST
Need ASAP please help
Answer:
POSSIBLY 1
Step-by-step explanation:
Please help im lost..
Answer:
c
Step-by-step explanation:
Solve for x. Show all your steps/work.
(¼)x + 1 = 22x
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
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
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.
Answer: $15,700 - $24,322= 8622
Step-by-step explanation:
All you have to do is subtract
Solve for angle B, then side a. Round to the nearest tenth.
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?
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
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HELP ME FOR 5 AND 6 PLEASEEEEE HDJSHSHS
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
Please help me with this homework
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
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
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
Pls Help Asap pls T^T
Answer: think its c
Step-by-step explanation:
I believe the answer is 18%
Simplify.
27²=
FAST plsssssssssssssssssssssss
Answer:
729
Step-by-step explanation:
27²= (27)(27)=729
6x+?= 10x
6x−?= 2x
6x+?= 2x
6x−?= 10x
6x+?=- 10x
6x−?= x
6x+?= 0
6x−?= 6
6x+?= 10
6x−?= 4x - 10
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
slope: -1 intercept: -7.9
what is the slope of each line that passes through the points?
what is the answer
Answer:
-1
Step-by-step explanation:
Since the question LITERALLY stated the slope is -1, the slope is literally -1
what is the volume of this pyramid?
the options are
A. 720
B. 1080
C. 1440
D. 2160
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.
Answer:
Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases.
Step-by-step explanation:
1.) find the first four terms in ascending powers of X in the expansion (2+2X)¹² .show your working!!
Answer:
15/8
Step-by-step explanation:
Simplify the expression: 4(x + 3) = 40
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
PLZS HELP THIS IS MY LAST QUESTION!!
Answer:
x = 30Step-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
Choose a positive number. Using this number as
the base, evaluate it when the exponent is 3,0,
and -2. Show all work.
Answer:
Step-by-step explanation:
Choose 3.
3^3 = 27;
3^0 = 1; and
3^(-2) = 1/9
Mr. Henry spent $15 on a new hat this week. He learned that the same hat available on
sale at $12 last week. What was the percentage increase in the price of the hat this
week?
HELP OMG
I LOST MY AIRPODS AT SCHOOL
Answer:
how should we help?
Step-by-step explanation:
Answer:
dang that sucks..... try and play music at max vol and see if you hear any music coming from anywhere that's probably were the airpods are, if they are in the case then i dont know if u would hear anything. It all depends...
~ i hope this has helped ya out some how, hope ya find your airpods my friend!~
Step-by-step explanation:
Help please!!!
Find the value of x. If necessary, write your answer in simplest radical form.
24
20
Answer: 46 is your answer hope this helped
Step-by-step explanation:
Answer:
[tex]4 \sqrt{11} [/tex]
Step-by-step explanation:
According to Pythagoras Theorem,
[tex] {(hypotenuse)}^{2} - {height}^{2} = {(base)}^{2} [/tex]
[tex] = > {24}^{2} - {20}^{2} = {x}^{2} [/tex]
[tex] = > \: {x}^{2} = 576 - 400[/tex]
[tex] = > {x}^{2} = 176[/tex]
[tex] = > x = \sqrt{176} [/tex]
[tex] = > x = \sqrt{2 \times 2 \times 2 \times 2 \times 11} [/tex]
[tex] = > x = 2 \times 2 \sqrt{11} [/tex]
[tex] = > x = 4 \sqrt{11} (ans)[/tex]
Find the area of the largest square contained by a circle of radius r = 1cm. Explain your answer and justify that it is correct. Hint: Use the pythagorean theorem.
Answer:
2 square cm
Step-by-step explanation:
Given :
A square is inscribed in a circle whose radius is r = 1 cm
Therefore, the diameter of the circle is 2 r = 2 x 1
= 2 cm.
So the diagonal of the square is 2r.
Using the Pythagoras theorem, we find each of the side of the triangle is [tex]$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.
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?
Answer: 18
Step-by-step explanation: