Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5? Why?
a. The matrix must have nothing pivot columns. If A had fewer pivot columns, then the equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements "A has a pivot position in every row" and "the columns of A span " are logically equivalent.
c. The matrix must have nothing pivot columns. Otherwise, the equation A would have a free variable, in which case the columns of A would not span .
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent
Answers
Answer:
The answer is "Option B".
Step-by-step explanation:
In the given choices there is some mistake so, the correct choice can be defined in the attached file. please find it.
In the given question, If the column of [tex]5 \times 7[/tex] matrix, and the A span is equal to [tex]R^5[/tex], and then the value of A has a pivot in each row, that's why in each pivot its position in the different columns of A has the five pivot columns, that's why the choice B is correct.
Related Questions
Please Solve as Fast as You Can
If the point (3, -2) is reflected across the y-axis, what are the coordinates of the reflected point?
Answers
Answer:
flips the sign of the opposing coordinate (-3,-2)
Step-by-step explanation:
An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answers
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
Einstein's equation relating mass and
energy is given by the formula E = mc,
where m is the mass of an object and
<= 3 x 10 ms', the speed of light.
a Find how much energy is present in
a 1 kg mass. (1 kg ms-'= 1 joule)
(2 marks)
Answers
Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and
placed in a hat. One piece of paper is randomly selected from the hat. Use the Venn diagram shown
to help you determine the probability that the number selected is odd or less than 5.
Answers
Step-by-step explanation:
i dont see a venn diagram but i think the number is probably more than 5
The probability that the number selected is odd or less than five will be 0.20 or 20%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and placed in a hat.
One piece of paper is randomly selected from the hat.
Then the probability that the number selected is odd or less than 5 will be
Total event = 10
Favorable event = 2 {1, 3}
Then the probability will be
[tex]\rm P = \dfrac{2}{10}\\\\P = 0.2 \ or \ 20\%[/tex]
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What is |5 x -3|?
-15
⊝
-8
⊝
15
⊝
8
Answers
Answer:
Step-by-step explanation:
Gfggg
if you can help i’d appreciate it
Answers
Answer:
B- 44
Step-by-step explanation:
87.5 divided by 2 is 43.75. Since it's a square wall, the length and height are both the same, and since length times height is area, if you divide the area by two, you can get a length of one of the sides. Out of all the answers, 44 is the closest to 43.75.
hope this helped! -brooke :))
is 13.48 irrational or rational?
Answers
Answer:
It is irrational
Step-by-step explanation:
Rational numbers do not have decimals.
Three cats and three dogs, A, B, C, D, E, and F, live on a street in three different-coloured houses. Each house hosts one cat and one dog. One house is red. A is a cat and does not live in the red house. B is a dog and does not live in the same house as C (even though they could). D lives in the blue house. D does not live with A or F (even though it could). E does not live with A and does not live in the yellow house.
Indicate whether each letter correspond to a cat or a dog, and match each cat and each dog with a colored house.
Answers
Answer:
1) A is a cat; B is a dog; C is a cat; D is a dog; E is a dog; F is a cat
2) A lives with B in a yellow house; C lives with D in a blue house; E lives with F in a red house.
Step-by-step explanation:
Step 1: First we identify the animals as cats or dogs
A is a cat
B is a Dog
Since B can live with C, C is a cat
Since D can live with A, D is a dog
F is a cat since it can live with D
E is therefore, a dog
Step 2: We then identify the house each two animals live in pairs of a cat and a dog
D lives in a blue house
A lives in a yellow house since it does not live with D or in a red house
C lives with D in a blue house since D does not live with either A or F
E lives in a red house since it does not live with A or in a yellow house
F lives with E in a red house since E does not live with A
Therefore, B lives with A in a yellow house
In how many ways 50 people can handshake with each other?
Answers
Answer:
My estimate think it 1225
Step-by-step explanation:
49 / 2 * (49 + 1) = 1225
Divide -3 3/4 divided by 3=?
Answers
The answer to your question is -1/4
x+2x+x+20=180 what is x
Answers
Answer: x=40
Step-by-step explanation:
x+2x+x+20=180
first you combine the like terms which are (x, 2x, x) and get 4x.
now you have 4x+20=180
next you subtract 20 on both sides:
4x+20=180
-20 -20
and get 4x=160
finally you divide 4 on both sides and get a final answers of x=40
A solid is formed by rotating the region bounded by the curve y = e^-3x/2 and the x axis between x=0 and x=1 around the xaxis. The volume of this solid is pi/3 * (1 - e^-3). Assuming the solid has constant density delta, find x and y.
x=
y =
Answers
Answer:
x = .28
y = 0
Step-by-step explanation:
Voume of disk = pi *r^2 = pi * e^-3x deltax
x = integal 0 to 1 of x * delta*pi*e^-3x deltax / mass = (delta*pi) integal 0 to 1 of x * e^-3x deltax/mass = (delta*pi)0.08898/mass
mass = sigma *(volume)=delta(pi/3*(1-e^-3)) =delta(.995)
x = (delta*pi)0.08898/delta(.995) = .28
by symmetry y=0
A solid is formed by rotating the region bounded by the curve y = e^-3x/2 and the x axis between x=0 and x=1 around the x axis. Then value of x is 0.28 and y is 0.
What is Volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
The volume of disk is given by formula πr²
Volume of disk = πr²= π × e⁻³ˣ Δx
[tex]x=\int\limits^0_1 {x} \, \pi e^{-3x} dx[/tex]
= (delta.π) integal 0 to 1 of x × e⁻³ˣ delta x/mass
= (delta. π) 0.08898/mass
mass = sigma ×(volume)=delta( π/3*(1-e⁻³)) =delta(0.995)
x = (delta*π)0.08898/delta(0.995) = 0.28
x=0.28
and by symmetry y=0
Hence the value of x is 0.28 and value of y is 0.
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A group of students went on a field trip to the zoo. 12 students went to the tiger exhibit. 4 students went to the gorilla exhibit. What is the ratio of students who visited the tigers to students who visited the gorillas?
Answers
Answer:
Tiger=12
glorillas=4
ratio=12\4
=4:1
Daniel has 15 yards of fabric to make baby blankets. It takes 1 and 1/2 yards of fabric to make each blanket, and the expression that models the situation is 15 minus three-halves y. Which of the following are possible numbers of blankets that Daniel could make? Select all that apply.
Answers
Answer:
any number between 0 and 10
Step-by-step explanation:
15 - 3/2y
how many times can 3/2 go into 15?
10 times. The most blankets he can make is 10, so any number less than 10 and greater than zero would be a correct solution
can i get brainliest please?
Answer:
9 and 10
Step-by-step explanation:
For each of the following cases [(a), (b), and (c)], (I) state whether the study should be observational or experimental. (II) state whether the study should be run blind, doubleblind, or neither. If the study should be run blind or double-blind, who should be blinded?(a) An investigation of whether taking aspirin reduces one’s chance of having a heart attack.(b) An investigation of whether babies born into poor families (family income below $25,000) are more likely to weigh less than 5.5 pounds at birth than babies born into wealthy families (family income above $65,000).(c) An investigation of whether the size of the midsagittal plane of the anterior commisssure (a part of the brain) of a man is related to the sexual orientation of the man.
Answers
Answer:
(a) An investigation of whether taking aspirin reduces one’s chance of having a heart attack.
Experimental
Neither blind nor double-blind (unless a placebo is being administered to some participants).
(b) An investigation of whether babies born into poor families (family income below $25,000) are more likely to weigh less than 5.5 pounds at birth than babies born into wealthy families (family income above $65,000).
Observational
There is no blinding issue here.
(c) An investigation of whether the size of the midsagittal plane of the anterior commissure (a part of the brain) of a man is related to the sexual orientation of the man.
Observational
There is no blinding issue here.
Step-by-step explanation:
An observational study happens where some variables are observed to determine their correlations. On the other hand, in experimental studies, the researcher controls certain variables to determine causality. Therefore, an experimental study provides evidence of cause and effect, like in (a) above.
In which of the following stores would you pay the least amount for an item that is priced $360?
Store A: Sale of 10% off and a successive discount of 10% off.
Store B: Sale of 15% with no additional discount.
Store C: Sale of $35 off and a successive discount of 10% off.
a.
All of the stores have the same discounted price.
b.
You can get the lowest price at Store A.
c.
You can get the lowest price at StoreB.
d.
You can get the lowest price at Store C.
Please select the best answer from the choices provided
A
B
C
D
Answers
''Store A'' has the least amount to pay for an item at price of 291.60.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Price : 360
Hence,
Store A: Sale of 10% off and a successive discount of 10% off.
360 x (100-10)% = 360 x 90% = 324
324 x (100-10)% = 324 x 90% = 291.60
Store B: Sale of 15% with no additional discount
360 x (100-15)% = 360 x 85% = 306
Store C: Sale of $35 off and a successive discount of 10% off
360 - 35 = 325
325 x (100-10)% = 325 x 90% = 292.50
Hence, Store A has the least amount to pay for an item at price of 291.60
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Jane has LaTeX: 2\frac{1}{2}2 1 2 cups of sugar. A recipe calls for LaTeX: \frac{1}{4}1 4 cup of sugar. How many recipes can she make?
Answers
Answer:
THERE IS NO RESULTS IN MY MIND
Step-by-step explanation:
SORRY IF WE DID NOT ANSWER IT SAD.......
insert 6 A . M's between 15 and -13
Answers
Answer:
15, 11, 7, 3, -1, -5, -9, -13
Step-by-step explanation:
Inserting Arithmetic Means (AM's)
Suppose we want to insert n equally-spaced numbers inside a given interval with endpoints [x,y].
To place n numbers, we need to open n+1 spaces, at the end of which, a new number will be placed. The given interval is then divided into n+1 rational numbers of a value (y-x)/(n+1).
We need to insert 6 AM's between 15 and -13. Each AM will be inserted at a space of (-13-15)(6+1)=-28/7=-4.
Thus the sequence is formed subtracting 4:
15
15-4=11
11-4=7
7-4=3
3-4=-1
-1-4=-5
-5-4=-9
-9-4=-13
The sequence is (numbers in bold are the AM's):
15, 11, 7, 3, -1, -5, -9, -13
Can u please helppppppp !!!!!!!!!
Answers
Answer:
yes i can help you
Step-by-step explanation:
Answer:
The height is the water wheel diameter so if you have 9' of head but are only running a 6 foot diameter wheel the height for this calculation is 6 feet. Most people use 12v batteries to store their electricity and an inverter
Step-by-step explanation:
Sorry if I cant help but that's number 2 answer.
Simplify the following expression, 3/8 divided by 1/4
Answers
The required simplified product is 3/2.
Given that fractions 3/8 ÷ 1/4.
To divide two fractions by multiplying the first fraction with the reciprocal of the second fraction.
Let a, b, c and d be any real numbers. Consider a/b ÷ c/d that gives
[tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{c}{d}[/tex].
That implies, [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{8}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{3}{2}[/tex].
Hence, the required simplified product is 3/2.
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A cookbook originally cost $13.00. Yesterday, Marta bought it at 40% off.
Horn
40%
OFF
How much was deducted from the original price? (4 pt.)
А
$0.40
B
$5.20
$7.80
Answers
A percentage is a way to describe a part of a whole. The amount paid by Marta for the cookbook is $7.80.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As it is given that the original price of the cookbook was $13, Marta bought it for 40% off. Therefore, Marta only paid 60% of the original cost,
[tex]\text{Amount paid by Marta} = \text{60\% of the original cost}\\\\\text{Amount paid by Marta} = \dfrac{60}{100} \times \$13\\\\\text{Amount paid by Marta} = \$7.8[/tex]
Thus, the amount paid by Marta for the cookbook is $7.80.
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i need help please help me
Answers
Answer:
use a contractor or protractor or whatever theyre called
Step-by-step explanation:
i just need points to ask another question
find an equation for the line that passes through the point (7,1) and is perpendicular to the line x-3y+25=0
Answers
Answer:
y + 3x = - 20
Step-by-step explanation:
x - 3y + 25 = 0
- 3y = - 25 - x
3y = 25 + x
y = ( 25 + x )/3
y = ( 1/3 )x + 25/3
Y= mX+ c
m= gradient= 1/3
The perpendicular gradient should be the negative reciprocal of the gradient we have now.
which is : -1÷(1/3) = -3
Now for the perpendicular line equation, we have:
y = 1
x= 7
m= -3
y - y1 = m ( x - x1 )
y - 1 = -3 ( x + 7 )
y-1 = -3x -21
y + 3x = -20
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Answers
Answer:
Y= -6x + 1
Step-by-step explanation:
Y=mx + b
M is your slope
B is your y intercept
Solve for X please :(( Will give brainliest.
Answers
5x+6+92 = 22x-4
5x+98 = 22x-4
add 5x to both sides
98 = 27x-4
add 4 to both sides
102 = 27x
divide both sides by 27
x = 3 and [tex]\frac{7}{9}[/tex]
what is 3/7 × 3 3/7?
Answers
= 3/4 × 3 3/7
= 3 3/7 as an improper fraction = 24/7
= 3/4 × 24/7
= 3 × 24 / 4 × 7
= 72/28
Let us try to simplify it .
We know that both 72 and 28 is divisible by 4 . Hence ,
72 ÷ 4 / 28 ÷ 4
= 18/7
Therefore , 3/7 × 3 3/7 = 72/78 or 18/7 ( simplest form ) .
Answer: 1²³⁄₄₉
Step-by-step explanation:
Convert any mixed numbers to fractions
3³⁄₇ x ²⁴⁄₇
Applying the fractions formula for multiplication
3 x 24
_____
7 x 7
= ⁷²⁄₄₉
Simplifying fraction
1²³⁄₄₉
[tex]lx+3l \leq 5[/tex]
Answers
9514 1404 393
Answer:
-8 ≤ x ≤ 2
Step-by-step explanation:
We assume you intend the absolute value equation ...
[tex]|x+3|\le5\\\\{-}5\le x+3\le5\qquad\text{rewrite as a compound inequality}\\\\\boxed{{-}8\le x\le2}\qquad\text{subtract 3}[/tex]
This is for 11th grade math
Answers
The equation y= 10x represents a proportional relationship what is the constant of proportionality
Answers
Answer:
constant of proportionality = 10
Step-by-step explanation:
Direct proportion equation :
y = kx, where k is the constant of proportionality
stare the property used in each case 13×11=11×13
Answers
Answer:
Commutative property of multiplication.
Explanation:
Commutative property is when you switch the order of the numbers around yet the answer still remains the same.
Ex: ab=ba or a+b=b+a