Please help! Correct answer only, please! Given matrix A and B both have dimensions 2 x 2 and are the inverse of one another what should be the following product? A · B A. B. C. D.

Please Help! Correct Answer Only, Please! Given Matrix A And B Both Have Dimensions 2 X 2 And Are The

Answers

Answer 1

Answer:

Option B.

Step-by-step explanation:

Let the two matrix A and [tex]A^{-1}[/tex] are,

A = [tex]\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}[/tex] and [tex]A^{-1}[/tex] = [tex]\frac{1}{(-1)}[/tex][tex]\begin{bmatrix}2 &-3\\-3 & 4\end{bmatrix}[/tex]

Therefore, [tex]A^{-1}[/tex] = [tex]\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}[/tex]

Now [tex]A.A^{-1}[/tex] = [tex]\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}.\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}[/tex]

                   = [tex]\begin{bmatrix}(-8+9) & (12-12)\\(-6+6) & (9-8)\end{bmatrix}[/tex]

                  = [tex]\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}[/tex]

Therefore, Option (B) will be the answer.


Related Questions

at a school number of boy:number of girls is in the ratio 11:9
there are 124 more boys than girls
work out the total number of sutdents at the school

Answers

Answer:

1240 (I'm not so sure but per my calculation that is what i got)

Step-by-step explanation:

Boy     : Girl

11         :   9

124 + x :  x

11/9 = 124 + x / x

9(124 + x) = 11 x

1116 + 9x = 11x

1116 = 11x - 9x

1116 = 2x

x = 558

Thus, there are 558 girls in the school

Number of boys = 124 + x

                             = 124 + 558

                             = 682

Therefore, total number of students = 558 + 682 = 1240 students

A ladder is leaning against a wall. The length of the ladder is 15 meters and
the base of the ladder is placed 9 meters away from the wall. How far up
the wall will this ladder reach?

A.) 6 m
B.) 10 m
C.) 12 m
D.) 18 m​

Answers

Answer:

the ladder is “c2” 15 X 15 =225

9 feet out is still squared to 81.

So c2 (225) - b2 (81) is 144 (a2)

Sqrt of 144 is 12. The ladder will be 12′ up the wall.

Answer: 12m

Step-by-step explanation:

P.S I'm emo

The height of a trapezoid is 4 in. And its area is 48 in 2. One base of the trapezoid is 6 inches longer than the other base. What are the length of the bases? Complete the explanation on how you found your answer

Answers

Answer:

9 inches and 15 inches

Step-by-step explanation:

The height of a trapezoid is 4 in.

Its area is 48 in^2.

Let a be one base and b be the second base.

One base is 6 inches longer than the other. This implies that:

a = 6 + b _________ (1)

The formula for the area of a trapezoid is given as:

[tex]A = \frac{1}{2}(a + b)h[/tex]

where h = height

From (1), we have that:

[tex]A = \frac{1}{2}(6 + b + b )h\\ \\A = \frac{1}{2}(6 + 2b )h[/tex]

We have that h = 4 and A = 48 in^2, therefore:

[tex]48 = \frac {1}{2}(6 + 2b) * 4\\ \\96 = 24 + 8b\\\\8b = 96 - 24 = 72\\\\b = 72 / 8 = 9 in[/tex]

=> a = 6 + 9 = 15 in

The bases are 9 inches and 15 inches long.

Which set of properties describes a square?

Answers

Answer:a parallelogram with one right vertex angle and two adjacent equal sides. a quadrilateral with four equal sides and four right angles. a quadrilateral where the diagonals are equal and are the perpendicular bisectors of each other, i.e. a rhombus with equal diagonals.

Step-by-step explanation:

El triple de la cuarta parte de un número es 18. ¿Cuál es este número?

a)24
b)72
c)48
d)12
e)6

Answers

Answer:

e) 6

Step-by-step explanation:

18 divided by 3 equals 6

which counterexample shows that the conjecture "all mammals live on land" is false?

Answers

Answer:

B. A whale is a mammal that does not live on land.

Step-by-step explanation:

Self explanitory

LAST TRY!!!! I HAVE THIS LAST QUESTION AND 4 MIMNTES LEFT!!!!!! PLS HELP OUT!!! WILL GIVE BRANLIEST!!! AT LEAST TAKE A LOOK!!! SHARE YO SMARTNESS! ONLY IF YOUR 100% SURE!

Which angles would apply to the consecutive exterior angles theorem?

A) 1 and 7; 2 and 8
B) 1 and 8; 2 and 7
C) 1 and 5; 3 and 7
D) 2 and 6, 4 and 8

Answers

Answer:

Step-by-step explanation:

Consecutive exterior angles lie outside on the same side of a transversal.

So it should be 3,45 and 6

Write each ratio or rate as a fraction in simplest terms. 2) 51 minutes to 21 minutes

Answers

Answer:

[tex]\frac{17}{7}[/tex]

One term of (x+y)^m is 31,824x^18y^11
What is the value of m ?

Answers

Answer: The value of m is 29.

Step-by-step explanation:

Given that, One term of [tex](x+y)^m[/tex] is [tex]31,824x^{18}y^{11}[/tex]  ...(i)

We know that that (r+1)th term in [tex](a+b)^n[/tex] is given by :-

[tex]T_{r+1}=^nC_ra^{n-r}b^r[/tex]  ...(ii)

On comparing (i) with (ii) , we get

[tex]a= x \text{ and } b= y \\n-r =18 \text{ and } r=11\\n=m[/tex]

i.e.

[tex]m-r=18\Rightarow\ m-11=18\\\\\Rightarrow\ m=18+11=29[/tex]

Hence, the value of m is 29.

The ratio of boys to girls in a class is 4:5
A. What fraction of the class are boys?
B. What fraction of the class are girls?

Answers

Answer:

Boys = 4/9

Girls = 5/9

Step-by-step explanation:

You add the ratio parts to find what the fraction is over.

5 + 4 = 9

Then you just need to know which part is boys and which is girls.

Boys to Girls = 4:5

Therefore Boys = 4/9 and Girls = 5/9.

Fraction of the class are boys = 4/9

Fraction of the class are girls = 5/9

What is ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given:

ratio of boys to girls = 4:5

Now, total of the ratio is = 4+5 = 9

So, fraction of the class are boys = 4/9

and, fraction of the class are girls= 5/9

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Simplify this expression. (2/x-y) + (3/x+y) - (5/y+x) - (7x-9y/y^2-x^2) = ___________/ y^2 - x^2

Answers

Answer:

(5y-17x)/ (y^2-x^2)

Step-by-step explanation:

(2/x-y) + (3/x+y) - (5/y-x) - (7x-9y/y^2-x^2) =

Get a common denominator of y^2 - x^2

2/ (x-y) = -2 /( y-x) * (y+x)/(y+x)  = (-2y -2x) / (y^2 -x^2)

(3/x+y) = 3/ (x+y) * (y-x)/(y-x) = (3y-3x) /  (y^2 -x^2)

-5/(y-x) = -5/(y-x) *(y+x)/(y+x) = -5y-5x /  (y^2 -x^2)

- (7x-9y/(y^2-x^2) = -7x +9y/ (y^2-x^2)

Combine the numerators since the denominators are equal

-2y -2x +3y-3x-5y-5x-7x+9y

5y-17x

Put this over the denominator

(5y-17x)/ (y^2-x^2)

Answer:

[tex] \frac{ - 17x + 5y}{ {y}^{2} - {x}^{2} } [/tex]

Solution,

[tex] \frac{2}{x - y} + \frac{3}{x + y} - \frac{5}{y - x} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{2}{x - y} + \frac{3}{x + y} - \frac{5}{ - (x - y)} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{2}{x - y} + \frac{3}{x + y} + \frac{5}{x - y} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{2}{x - y} + \frac{5}{x - y} + \frac{3}{x + y} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{2 + 5}{x - y} + \frac{3}{x + y} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{7}{x - y} + \frac{3}{x + y} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{7(x + y) + 3(x - y)}{(x - y)(x + y)} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{7x + 7y + 3x - 3y}{ {x}^{2} - {y}^{2} } - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{10x + 4y}{ {x}^{2} - {y}^{2} } - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{10x + 4y}{ - ( {y}^{2} - {x)}^{2} } - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{ - 10x - 4y - 7x + 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{ - 10x - 7x - 4y + 9y}{ {y}^{2} - {x}^{2} } \\ = \frac{ - 17x + 5y}{ {y}^{2} - {x}^{2} } [/tex]

hope this helps...

Good luck on your assignment...

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99​% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.2 in. and a standard deviation of 1.2 in. Find Upper P 99. That​ is, find the hip breadth for men that separates the smallest 99​% from the largest 1​%.

Answers

Answer:

Upper P99 = 17 in.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 14.2, \sigma = 1.2[/tex]

Upper P99

This is X when Z has a pvalue of 0.99. So X when Z = 2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.327 = \frac{X - 14.2}{1.2}[/tex]

[tex]X - 14.2 = 1.2*2.327[/tex]

[tex]X = 17[/tex]

So

Upper P99 = 17 in.

Find the product of 3/8 and reciprocal of - 5/11​

Answers

[tex]reciprocal \: of \: \frac{ - 5}{11} \: is \frac{ - 11}{5} \\ product \: of \: \frac{ - 11}{5} \times \frac{3}{8} = \frac{ - 33}{40} \\ hope \: it \: helped \: [/tex]

hope it helps you if it does please mark me as brainliest :-)

classify the following triangle check all that apply

A.Isosceles
B.Scalene
C.Right
D.Obtuse
E.Acute
F.Equilateral​

Answers

Answer:

c.Right

Step-by-step explanation:

because of the 90 degrees it shows that it is 90 degrees

Answer:

B. scalene

C. right

Step-by-step explanation:

express 0.0043216 in standard form​

Answers

Answer:4.3216*10^-3

Step-by-step explanation:

Answer:

4.3216*10^(-3)

Step-by-step explanation:

Moving the decimal point 3 places to the right results in 4.3216*10^(-3), which is in standard form.

A group of 6 friends of varying ages meets at a coffee shop and sits in a circle. What is the probability that the
youngest member of the group sits in the seat closest to the door?

Answers

Answer:

[tex]100.00 \div 6 [/tex]

The probability that the youngest member of the group sits in the seat closest to the door 1 / 6

Given that, a group of 6 friends of varying ages meets at a coffee shop and sits in a circle, we need to find the probability that the youngest member of the group sits in the seat closest to the door,

So, the probability = favorable outcomes / total outcomes

Here, the favorable outcome = 1

The total outcomes = 1, 2, 3, 4, 5, 6 = 6

So, the probability = 1/6 = 1/2

Hence, the probability that the youngest member of the group sits in the seat closest to the door 1 / 6

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lainey bought a set of 15 makers for $6 what is the cost of 1 marker

Answers

Answer:

Each marker costs $.40 or 40 cents

Step-by-step explanation:

Take the total cost and divide by the number of markers

$6.00 /15

.40

Each marker costs $.40 or 40 cents

PLZ HELP I'VE BEEN STUCK FOR A LONG TIME PLZ HELP
(c-d)/5 - 2 = 0
c-6d=0
Given the equations, what is the value of c/d?
PLZ HELP WILL MARK BRAINLIEST

Answers

Answer:

c/d = 6

Step-by-step explanation:

Use the second equation.

c - 6d = 0

Add 6d to both sides.

c = 6d

Divide both sides by d.

c/d = 6

A bicycle wheel is 63 centimeters from top to bottom. When the wheel goes all the way around one time,the bicycle travels 198 centimeters. How can this information be used to estimate the value of

Answers

Divide the distance traveled by the wheel to guess the value or estimate the value of π.

What is a circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

Given

Height of the wheel = 198

Perimeter of the wheel = 63

Height of the wheel is the diameter of the circle

Perimeter of the circle is  π × diameter of the circle

P = [tex]\pi[/tex] × d

198 = [tex]\pi[/tex] × 63

[tex]\pi[/tex] = [tex]\frac{198}{63}[/tex]

[tex]\pi[/tex] = 3.14

Hence, Divide the distance traveled by the wheel to guess the value or estimate the value of π.

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Work out
3/4 times 1/2

Answers

Answer:

[tex]\frac{3}{4} * \frac{1}{2} = \frac{3}{8}[/tex] alternatively, the answer is 0.375

5 (2 x +1)-2=6x+5
Can someone help solve this

Answers

x= 1/2 or 0.5
hope this helps
Exact form is x=11/2
Decimal form x=5.5
Mixed number form x=5(1/2

What is 9/2 in a percentage

Answers

Answer:

450%

Step-by-step explanation:

Answer:

450%

Step-by-step explanation:

Please help me!!!!!!

Answers

Answer:

16.7 cm

Step-by-step explanation:

So B = 180 -A-C=180-58-75=47degree

sinB/AC = sinC/AB

sin47/AC=sin75/22

AC=16.65cm

Simplify the Algebraic Expressions Problems 15 - 19.

15. 7c + 8d + 2c + 17d =

16. 4(2m - 3p) + 12m + 7p =

17. (15j +9z) - (12j + 6z) =

18. 3y + 6.7x + y + 2.3x +10 - 7 =

19. 2b + (-6c) +5e - 11b + e+ 6c =

Answers

Answer: The answers are provided below

Step-by-step explanation:

15. 7c + 8d + 2c + 17d

= 7c + 2c + 8d + 17d

= 9c + 25d

16. 4(2m - 3p) + 12m + 7p

= 8m - 12p + 12m + 7p

= 8m + 12m -12p + 7p

= 20m - 5p

17. (15j +9z) - (12j + 6z)

= 15j - 12j + 9z + 6x

= 3j + 15z

18. 3y + 6.7x + y + 2.3x +10 - 7

= 6.7x + 2.3x + 3y + y + 10 - 7

= 9x + 4y + 3

19. 2b + (-6c) +5e - 11b + e+ 6c

= 2b - 11b - 6c + 6c + 5e + e

= -9b + 6e

help me hahahahahahhahahahaha

Answers

Pretty sure it’s 3x=3


PLEASE HELP! WILL MARK BRAINLIST!!!

Find the volume of the sphere. Either enter an exact answer in terms of π or use 22/7 for pi. (radius is 1/2)

Answers

Answer:

1/6π units³ or 11/21 units³

Step-by-step explanation:

V = 4/3 πr³

r= 1/2

V= 4/3π* (1/2)³= 1/6π

or

V= 1/6 *22/7= 11/21

Answer:

1/6

Step-by-step explanation:


Express 250 ml as a percentage of 2 litres.​

Answers

1 litre= 1000mL

Given: 2 liters

2×1000= 2000 litre

Now to find %

250/2000 × 100

Answer: 12.5%

Please answer correctly !!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!

Answers

Answer:

x = -3/2                    x =0

Step-by-step explanation:

(2x+3) ^2 - 6x-9 = 0

Factor out -3 from the last 2 terms

(2x+3) ^2 - 3( 2x+3) = 0

Let m = 2x+3

m^2 - 3m = 0

Factor out m

m(m-3) =0

Using the zero product property

m=0  m-3 =0

m=0  m=3

Substitute 2x+3 back in for m since we are looking for the value of x

2x+3 =0                2x+3 =3

2x +3-3=0-3       2x+3-3=3-3

2x = -3                  2x=0

x = -3/2                    x =0

5/4 x (54/48 + 105/75)

Answers

Answer:

  5/4 x (54/48 + 105/75)

=  5/4 x (9/8 + 7/5)

=  5/4 x (45/40 + 56/40)

=  5/4 x 101/40

=  1/4 x 101/8

=  101/32

Hope this helps!

:)

Answer: 3/5/32

Step-by-step explanation:

5/4 x(54/48 + 105/75)

5/4 x (1/1/8 + 1/2/5)

5/4 x 2/21/40

1/1/4 x 2/21/40

3/5/32 ( 3 whole and 5 over 32)

HOPE THIS HELPS

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Find the indicated term of the given arithmetic sequence.

a14 for 200, 196, 192, ...

Answers

Answer:

148

Step-by-step explanation:

AP 200, 196, 192, ...

a14=?

---------

a1= 200

d= 196-200=192-196= -4

a14= a1+13d

a14= 200+13*(-4)= 200- 52= 148

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