Assume that the matrices below are partitioned conformably for block multiplication. Compute the product.

[I 0] [W X]
[K I] [Y Z]

Answers

Answer 1

Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

(I assume I is the identity matrix and 0 is the zero matrix.)


Related Questions

Find the missing segment in the image below

Answers

Answer:

4

Step-by-step explanation:

First, we can take two triangles -- one with 2 as a side and the big one. Literally every side of the triangle with the 2 in it is parallel to its corresponding side the big triangle. Therefore, we can say that the two triangles are similar.

In similar triangles, we can say that the ratios of corresponding sides are the same. Let's say that the bottom side of the big triangle is x, and the question mark is y. Therefore, the hypotenuse of the big triangle is 6+y. Furthermore, the ratio of corresponding sides ((6+y)/y and x/2) are equal, so

(6+y)/y = x/2

Since x is clearly made up of 3 and 2, we can say 3+2=x=5

(6+y)/y = 5/2

multiply both sides by y to remove a denominator

6+y = 5*y/2

multiply both sides by 2 to remove the other denominator

12+2y = 5*y

subtract both sides by 2y to isolate the y and its coefficient

12 = 3y

divide both sides by 3 to isolate the y

y=4

the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age?​

Answers

Answer:

sadia is 32

Step-by-step explanation:

sadia : father : total

3          6          9

Divide 96 by 9

96/9 = 32/3

Multiply each by 32/3

sadia :     father : total

3*32/3    6*32/3  9*32/3

32                 64          96

Which describes the correlation shown in the scatterplot?

On a graph, points are grouped closely together and increase.
There is a positive correlation in the data set.
There is a negative correlation in the data set.
There is no correlation in the data set.
More points are needed to determine the correlation.

Answers

Answer:

More points are needed to determine the correlation.

Answer:

its d

Step-by-step explanation:

;)

PLZ ANSWER QUESTION IN PICTURE

Answers

Answer: y = 3x + 6

Step-by-step explanation:

(x-intercept of -2: (-2,0))

(slope = m)

y = mx + b, (-2,0), m = 3

[tex]y=mx+b\\0=3(-2)+b\\0=-6+b\\b=6\\y=3x+6[/tex]

Help! Please? Dont understand

Answers

The answer for this is B

180 °
35 °
X °

X = ? °

Answers

Answer:

x=145°

Step-by-step explanation:

180 = 35 + x

x = 180-35

x= 145°

find the area of the regular polygon​

Answers

Answer:

A = 374.123 ft^2

Step-by-step explanation:

First, lets calculate the perimeter:

Perimeter (p) = side length (s) * number of sides (n)

[tex]p = s * n[/tex]

[tex]p = 12 * 6[/tex]

[tex]p = 72[/tex]

Next, lets find the apothem, which is the shortest length from any side to the middle. It's like the radius in a circle, but more complicated.

Apothem (a) = side length (s) / ( 2 * tan(180/number of sides (n)) )

[tex]a = \frac{s}{2 * tan (\frac{180}{n} )}[/tex]

[tex]a = \frac{12}{2 * tan (\frac{180}{6} )}[/tex]

[tex]a = \frac{12}{2 * \frac{\sqrt{3} }{3}}[/tex]

[tex]a = \frac{12}{\frac{2\sqrt{3} }{3}}[/tex]

[tex]a = \frac{12*3}{2\sqrt{3}}[/tex]

[tex]a = \frac{6*3}{\sqrt{3}}[/tex]

[tex]a = \frac{18}{\sqrt{3}}[/tex]

Now, finally, to find the area of a regular polygon, we use the following equation:

Area (A) = ( apothem (a) * perimeter (p) ) / 2

[tex]A = \frac{a * p}{2}[/tex]

[tex]A = \frac{\frac{18}{\sqrt{3} } * 72}{2}[/tex]

[tex]A = \frac{18}{\sqrt{3}} * 36[/tex]

[tex]A = \frac{640}{\sqrt{3}}[/tex]

Turning into a decimal:

[tex]A = 374.123 ft ^2[/tex]

Giúp mình bài này với ạ

Answers

Could u explain in English

I need help completing this problem ASAP

Answers

Answer:

8 sqrt(5)

Step-by-step explanation:

sqrt(45) + sqrt(125)

Rewriting

sqrt(9*5) + sqrt( 25 *5)

we know sqrt(ab) = sqrt(a) sqrt(b)

sqrt(9) sqrt(5) + sqrt(25) sqrt(5)

3 sqrt(5)+5 sqrt(5)

Add like terms

8 sqrt(5)

Answer:

A.    [tex] 8\sqrt{5} [/tex]

Step-by-step explanation:

[tex] \sqrt{45} + \sqrt{125} = [/tex]

[tex] = \sqrt{9 \times 5} + \sqrt{25 \times 5} [/tex]

[tex] = 3\sqrt{5} + 5\sqrt{5} [/tex]

[tex] = 8\sqrt{5} [/tex]

Find perpendicular,hypotenuse and base​

Answers

Step-by-step explanation:

In right angled triangle ABC,

Taking alpha as reference angle,

By pythagoras theorem,

p=BC,h=AB,b=AC

Taking thita as reference angle,

p=AC,h=AB,b=BC

Keep smiling and hope u are satisfied with my answer.Have a good day :)

Knowing that AQPT - AARZ, a congruent angle pair is:

Answers

Answer:

Angle T is congruent to Angle Z

Step-by-step explanation:

Since the 2 triangles are equal, that means that each pair of angles are also congruent. To know which angles are congruent, you check th order of how the triangles are named. Ex. Angle Q is congruent to Angle A, Angle P is congruent to Angle R, and Angle T is congruent to Angle Z.

Two identical lines are graphed below. How many solutions are there to the
system of equations?
5
A. Infinitely many
B. Zero
C. One
D. Two

Answers

You’re best choice isB

Two identical lines have, A. Infinitely many solutions.

What are the three types of solutions for a system of linear equations?

If a system of equations only contains two linear equations with two variables,

The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given are two identical lines,

Now we know the solution of two lines is where they intersect.

We also know that a line is made up of infinite points, So if two lines are identical every point of one line lies with every other point of the other line.

Therefore they have an infinite number of solutions.

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3. A rectangular sheet of paper is 121/2 cm long and 102/3 cm wide. Find its perimeter .​

Answers

Answer:189 cm

Step-by-step explanation:

the area of a perimeter is 2L+2w while l is length and w is width

in this case, 121/2 is the length and 102/3 is the width.

using the formula it should be

121/2 x 2 +102/3 x

= 121 + 68

=189 cm

i hope this helps.

Which statements describe the data in the bar graph? Check all that apply.


People prefer rock music to any other type of music.

People prefer pop music to any other type of music.

The least favorite genre of music is blues.

The least frequent favorite genre is country.

Four times as many people prefer pop music to blues.

Answer:
People prefer pop music to any other type of music.

The least favorite genre of music is blues.

Four times as many people prefer pop music to blues.

Answers

Answer:

People prefer pop music to any other type of music.

The least favorite genre of music is blues.

Four times as many people prefer pop music to blues.

Answer:

B) People prefer pop music to any other type of music.

C) The least favorite genre of music is blues.

E) Four times as many people prefer pop music to blues.

Step-by-step explanation:

edge 2023

Let S be a sample of size 31 from a normally distributed population Omega . It is given that the average of the data in S is 120 and the standard deviation is 18. Construct a 90% confidence interval [a, b] for the population mean based on the data in the sample.

Answers

Answer:

48 NO seña hfjxsmisns sisbxbd

Step-by-step explanation:

nzhejsbxbddndbhwksdyanvxydjd4mnnneknwnennnnnn

Assuming boys and girls are equally​ likely, find the probability of a couple having a baby boy when their third child is​ born, given that the first two children were both boys

Answers

50% because the first two children have no effect on the third one

The required probability of a couple having a baby boy when their third child is​ born is 1/2.

What is probability?

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

Assuming boys and girls are equally​ likely.

The first two children were both boys

According to given question we have

The probability of having a baby girl is an independent probability.

The first two children were both boys

So, it is not related to the previous child.

So required probability = 1/2

Therefore, the required probability of a couple having a baby boy when their third child is​ born is 1/2.

Learn more details about probability here:

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(−x3+26x2−7x−13)+(6x4−x3+8x+27)

Express the answer in standard form.

Enter your answer in the box.

Answers

Answer:

6x^4−2x^3+26x^2+x+14

Step-by-step explanation:

−x^3+26x^2−7x−13+6x^4−x^3+8x+27

= 6x^4−x^3−x^3+26x^2−7x+8x−13+27

= 6x^4−2x^3+26x^2+x+14

Answer:

Step-by-step explanation:

= -x3+ 26x2- 7x-13+6x4-x3+8x+27

=6x4-2x3+26x2+x+14

What is the value of -
-X2 - 4x – 11 if x = -3?

Answers

the answer to this question is -8

Which table represents a linear function

Answers

Answer:

3rd option (top right)

Step-by-step explanation:

3rd option represents a linear equation

y = -2x-1

Answered by GAUTHMATH

Se practica un orificio circular de 2 cm de diámetro en la pared lateral de un gran depósito a una distancia de 10 m por debajo del nivel del agua. Calcule: a) la velocidad de salida, y b) el volumen que sale por unidad de tiempo. Sol. a) 14 m/s. b) 4.4 x 10-3 m3 /s

Answers

Answer:

I dont speak Spanish bro bro

A line passes through (-6,-5) and has the slope of 2/3

HELPPPP PLEASE!!

Answers

Answer:

y = 2/3x-1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2/3x +b

Using the point (-6,-5)

-5 = 2/3(-6)+b

-5 = -4 +b

Add 4 to each side

-5+4 = b

-1 =b

y = 2/3x-1

Answer:

[tex] y = \frac{2}{3}x - 1 [/tex]

Step-by-step explanation:

[tex]y = mx + c \\ \\ m = slope \\ c = y \: \: intercrept[/tex]

[tex]m = \frac{2}{3} [/tex]

[tex]y = mx + c \\ - 5 = \frac{2}{3} \times - 6 + c \\ - 5 = \frac{ - 12}{3} + c \\ - 5 = - 4 + c \\ - 5 + 4 = c \\ - 1 = c[/tex]

So, the equation of the line is,

[tex]y = mx + c \\ y = \frac{2}{3}x - 1 [/tex]


(a) Joe runs 12 miles in 84 minutes.
How many miles does he run per minute?
İmiles per minute

Answers

Step-by-step explanation:

We want to find how many miles per minute Joe runs. This means, we need to simplify the equation:

[tex]\frac{12 mi}{84 min}[/tex]

so that the number on the bottom is 1. How do we do that?

Simple.

Just divide 12 / 84

Answer:

Joe runs approx. 0.143 miles per minute.

Can someone do these please? ❤️

Answers

Answer:

-49

8

Step-by-step explanation:

-196/4 =

-49

(3+u)^2

-------------

8

Let u=5

(3+5)^2

-------------

8

(8)^2

-------------

8

64

-----

8

8

A triangle. A ABC, has angle measures of 82*, 75, and 23' and no sides equal (congruent) in length. How would this triangle be
classified?
Equilateral right
Isosceles obtuse
O Scalene acute
Isosceles acute

Answers

The triangle given is a scalene acute triangle

Classification of Triangle

A triangle can be classified based on the measures of its angles and the lengths of its sides.

In this case, the angle measures of the triangle are 82, 75, and 23 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can verify that these angles satisfy this condition: 82 + 75 + 23 = 180.

The triangle is not an equilateral triangle because all the sides are not of equal length.

The triangle also doesn't have one right angle so it can't be right triangle.

Now, as per the angle measures, none of the angles are right angles, but one angle is greater than 90 degree, so this triangle is not acute triangle.

So, this triangle is not an Obtuse triangle since it has no angle greater than 90 degrees.

As the triangle has no sides of equal length, it is also a Scalene triangle.

Therefore, the triangle would be classified as a Scalene acute triangle (c).

Learn more on classification of triangle here;

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Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
O A. 1
ОВ. о
C. infinitely many
O D. cannot be determined
SURAT

Answers

Answer:

C. infinitely many

Step-by-step explanation:

If two equations in slope-intercept form have the same slope and y-intercept they must be the same line. Additionally, the solutions of a system of equations are wherever the two lines intersect. Since the lines are the same they must intersect at every point. Therefore, there are infinitely many solutions.

If a household appliance has a wattage of 1,892 and is in use for 5, how much CO2 was produced? Round to 1 decimal.​

Answers

Answer:

Step-by-step explanation:

dude what class?

50 students in a class were asked at the beginning of the week what they did at the weekend. 18 read their books, while 28 watched films, and 7 neither read their books nor watched films. How many students both read their books and watched films?​

Answers

Answer:

so 3 people both read their books and watched films.

Step-by-step explanation:

n(U) = 50

n(A) = 18 ( read books)

n(B) = 28 ( watched films)

n(A U B) with a line at the top = 7

so

Finding n(AUB)

n( A U B) with a line at the top = n(A) + n(B) - n( A n B)

7 = 50-n(A U B)

or, n( A U B) = 50 - 7

so, n(A U B) = 43

Then

n( A U B) = n(A)+n(B)-n(A n B)

43 = 18 + 28 - n( A n B)

or, 43 = 46 - n(A n B)

or, n(A n B) = 46 - 43

so, n(A n B) = 3

Can someone please do #3?❤️

Answers

Answer:

B, because it goes up by 8 until the last of because the jump from 24 to 30 is 6

It takes Jacob and Hannah a hours to do
a certain job, it takes Jacob and Ethan b
hours to do the same job and it takes
Hannah and Ethan c hours to do the
same job. How long would it take Jacob,
Hannah and Ethan to do the same job if
all of them worked together?

Answers

Step-by-step explanation:

Kym teaches sixth grade students in an urban school where most of the families in the community live below the poverty line. Each year the majority of the students in her school fail the statewide tests. Kym follows school district teaching guides and typically uses direct instruction in her Language Arts and Social Studies classes. The classroom assessments are designed to mirror those on the statewide tests so the students become familiar with the assessment format.

A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
A. −3x + 5y = 13
B. −3x + y = −7
C. −3x + y = 17
D. −3x + 5y = −13
Which answer is an equation in point-slope form for the given point and slope?
Point: (1, 9); Slope: 5
A. y − 1 = 5 (x + 9)
B. y − 9 = 5 (x − 1)
C. y + 9 = 5 (x−1)
D. y − 9 = 5 (x+1)

Answers

Answer:

−3x + y = −7       y - 9 = 5 (x - 1)

Step-by-step explanation:

y2 - y1 / x2 - x1

5 - (-1) / 4 - 2

6/2

= 3

slope intercept: −3x + y = −7

y - 9 = 5 (x - 1)

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