Which of the following sets of vectors in R3 are linearly dependent?
Note. Mark all your choices.
Answers
9514 1404 393
Answer:
B, C
Step-by-step explanation:
Linearly dependent sets can be found using row-reduction techniques. If a row ends up zero, then the set is linearly dependent. Equivalently, the determinant of a 3×3 matrix can be computed. If it is zero, the set is dependent. The cross-product of two 3-D vectors can be computed. If it is zero, the vectors are dependent.
Any set of vectors that has more elements than each vector does must necessarily be dependent.
It is helpful to be able to use a calculator capable of performing these calculations (as opposed to doing it by hand). The first attachment shows the result of computing the reduced row-echelon form of the first set of 3 vectors. The set is found to be independent.
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The second set of vectors is clearly dependent, as the second vector is 5 times the first.
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The third set contains more vectors than there are elements to a vector. Hence at least one of them can be created using some combination of the others. This set is dependent.
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The cross-product of the fourth set is non-zero, so it is independent. The second attachment shows the result of a row-reduction tool on these vectors.
Related Questions
Using the diagram, calculate the values of the unknown variables: a, b, and c.
Answers
Answer:
a = 82
b = 130
c = 118
Step-by-step explanation:
A quadrilateral is inscribed in a circle. So, it is a cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
a° + 98° = 180°
a° = 180° - 98°
a° = 82°
a = 82
By inscribed angle theorem:
a° = 1/2(b° + 34°)
82° * 2 = b° + 34°
164° - 34° = b°
b° = 130°
b = 130
Again by inscribed angle theorem:
76° = 1/2(c° + 34°)
76° *2 = c° + 34°
152° - 34° = c°
c° = 118°
c = 118
Sue at 30 cherries. She ate 5 times as many cherries as bob. How many cherries did bob eat
Answers
Answer:
6
Step-by-step explanation:
6 times 5 is 30. You would've divided 30 by 5
Explanation if she ate 30 and 5 time more then you need to divide
help its due in 1 hour !!!
Answers
Answer:
Hello its 78 I believe good luck!
Andy's age is 67, which is 17 less than 12 times bills age. What is bills age?
Answers
Bill is about 49 years old.
Answer:
7
Step-by-step explanation:
67 + 17 = 84
84/12 = 7
I was unsure if my answer was incorrect please help
Answers
Find the area of the smaller sector round to the nearest tenth. Need help fast!!
Answers
The area of the sector is 76. 95 m
How to determine the area of a sector
Using the formula;
Area of sector of a circle = /360° (r2)
where r is the radius of the circle
is the angle of the sector
From the diagram,
= 77°
r = 10. 7m
= 3. 142
Substitute into the formula
Area of the sector = 77/ 360° * (3. 142* 10. 7 * 10. 7)
Area of the sector = 0. 2139 * 359. 72
Area of the sector = 76. 95 m
Thus, the area of the sector is 76. 95 m
Learn more about the area of a sector here:
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Please help immediately !!
Answers
Marcie conducts an experiment with a bag of marbles. She draws one marble from the bag, records its color, returns the marble to the bag, and draws again. The results of her experiment are shown below.
Marble Color Number of
Times Drawn
red 5
blue 6
green 4
purple 1
yellow 4
Based on Marcie’s experiment, what proportion of the marbles in the bag would she expect to be purple?
A.
20%
B.
5%
C.
1%
D.
10%
Answers
Answer:
B. 5%
Step-by-step explanation:
add them:
5 + 6 + 4 + 1 + 4 = 20
now use it to divide from the number of times purple is drawn = 1 so,
1/20 = 0.05 = 5%
Tyra has 1223 cups of sugar. If r is the amount of sugar called for in one batch of cookies,
the expression 1223 ÷ r can be used to find how many batches Tyra can make with the sugar she has.
If r is 23 cup, how many batches of cookies can Tyra make?
Answers
Answer:
She can make 19 batches of cookies.
1.34 x 10^-2 to standard form
Answers
Answer:
1.34×10^-2 in standard form is 0.0134
The price of a necklace was increased by 10% to £121.
What was the price before the increase?
Answers
Answer:
£108.90
Step-by-step explanation:
[tex]121 \times 10\% \\ = 121 \times 0.10 \\ = 108.90[/tex]
Find each angle measure Make sure to give all 3
Answers
[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]
a) 34°
b) 90°
c) 30°
thankshope it helps.How many different meals can you order from a restaurant that has a menu with 8 appetizers, 3 entrees, 5 desserts, and 8 drinks? (Assume that you are getting one item from each section of the menu.)
Answers
8 x 3 x 5 x 8 = 960
Does anybody have the answer
Answers
Answer:
You're answer is right it is -2,2
Step-by-step explanation:
remember x comes before y
- En una tienda, durante las rebajas, encontramos los siguientes carteles: “ De 150 euros a 90 euros” y “De 40 euros a 24 euros”. ¿Tienen los dos artículos el mismo porcentaje de rebaja ?
Answers
Answer:dwadwdwd
Step-by-step sadawdwdwadwdwexplanation:
What is the surface area of the square pyramid, in square inches (Please Help)
Answers
Answer:
220.8 in.²
Step-by-step explanation:
Area of the pyramid = area of the square + 4(area of the triangle)
Area of square = s²
s = 9.2 in.
Area of the square = 9.2² = 84.64 cm²
✔️Area of the 4 triangles = 4(½*bh)
b = 9.2 in.
h = 7.4 in.
Area = 4(½*9.2*7.4) = 136.16 in²
✅Surface area = 84.64 + 136.16 = 220.8 in.²
The cost of interest of a $3,000 loan at 12% interest per year is $1003.80.
What is the term length for this loan in years?
Answers
9514 1404 393
Answer:
2.79 years
Step-by-step explanation:
If we assume simple interest, the interest amount is computed from ...
I = Prt
Then the length t is ...
t = I/(Pr)
t = 1003.80/(3000×0.12) ≈ 2.788333...
The term of the loan is about 2.79 years.
If you shift the linear parent function, f(x) = x, down 6 units, what is the
equation of the new function?
Answers
What is the mean for these numbers?
5,5,5,5
Answers
Answer:
IF THERE IS A LINK DON'T CLICK ON IT
Step-by-step explanation:
IT'S A COMPUTER PHONE AND TABLET VIRUS
Answer:
5
Step-by-step explanation:
A rectangular prism and its dimensions are shown in the diagram.
Dimensions:length 7.5 width 5 height 6.5
what is the total surface area
Answers
Answer:
237.5
Step-by-step explanation:
2·(5·7.5+6.5·7.5+6.5·5)=237.5
what is the
the distance between a point at (-3,4) and a point at (2,-5)
Answers
What is the distance between a point at (-3,4) and a point at (2,-5) ?
Solution:-Let the two points be A and B .
And, let the distance be P .
Now, the distance P between the point A (-3,4) and the point B (2,-5) is
[tex] \bf P \: = \sqrt{(-3 \: - \: 2)^2 \: + \: (4 \: + \: 5)^2} [/tex]
[tex] \implies [/tex] [tex] \bf P \: = \sqrt{(-5)^2 \: + \: (9)^2} [/tex]
[tex] \implies [/tex] [tex] \bf P \: = \sqrt{25 \: + \: 81} [/tex]
[tex] \implies [/tex] [tex] \bf P \: = \sqrt{106} [/tex]
[tex] \implies [/tex] [tex] \bf P \: = \: 10.3 [/tex]
The distance between a point at (-3,4) and a point at (2,-5) is 10.3 . [Answer]One year, the population of a city was 143,000. Several years later it was
138,710. Find the percent decrease.
Answers
Answer:
One year, the population of a city was 143,000. Several years later it was
138,710. Find the percent decrease - 3% decrease.
form the largest and the smallest 4 digit numbers using each of the digits 9,1,0,5 only once
Answers
Answer:
smallest: 1059
largest: 9510
Two students were asked if they liked to read. Is this a good example of a
Yes, this is a good statistical question because a variety of answers
Yes, this is a good statistical question because there are not a varie
No, this is not a good statistical question because there are not a
No, this is not a good statistical question because there are a van
Answers
Answer:
C. No, this is not a good statistical question because there are not a.
Step-by-step explanation:
Because you need a big amount of people to ask for it to be a A good statistical question.Your welcome! Please mark brainliest!
(Or please correct me if I'm wrong)
Each day for the next 4 days, there is a 20% chance of a thunderstorm. Use the simulation shown, where the digits 1 and 2 represent days with a thunderstorm, to estimate the probability of a thunderstorm on at least 2 of the next 4 days. Round your answer to the nearest tenth of a percent if necessary.
Answers
Answer:
It’s 6/1
Step-by-step explanation:
The estimated probability of a thunderstorm on at least 2 of the next 4 days is 6/16, or 0.375, or 37.5% (rounded to the nearest tenth of a percent).
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur.
To estimate the probability of a thunderstorm on at least 2 of the next 4 days, we can use the simulation as follows:
The outcomes with at least 2 thunderstorms are: 112, 121, 122, 211, 212, and 221.Out of the 16 possible outcomes (each day can either have a thunderstorm or not), the number of outcomes with at least 2 thunderstorms is 6.Therefore, the estimated probability of a thunderstorm on at least 2 of the next 4 days is 6/16, or 0.375, or 37.5% (rounded to the nearest tenth of a percent).Thus, this is only an estimate based on the given probability of a thunderstorm each day, and the actual probability may be different.
For more details regarding probability, visit:
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4.78 times 10 to the 6th power was the largest attendance record of the polar bear express. chilly football extravaganza. 3.98 times 10 to the 6th power attended at the last last pb express event. how many more people were in attendance on the record-setting day?
Answers
9514 1404 393
Answer:
8×10⁵ = 800,000
Step-by-step explanation:
The difference is ...
(4.78×10⁶) -(3.98×10⁶) = 0.80×10⁶ = 8×10⁵
8×10⁵ = 800,000 more people attended at the largest extravaganza.
_____
Your calculator (or a spreadsheet) can do the subtraction and display the number in whatever format you want.
what other classifications can a rhombus be
Answers
Answer:
Classification of rhombus
Step-by-step explanation:
The opposite angles of a rhombus are equal.each diagonal bisect the vertical angles.the diagonals are not equal and bisect each other perpendicularly.the triangles formed by the diagonals are congruent.the area of a rhombus=1/2d1×d2PLEASE HELPPP! I'LL GIVE BRAINLEST
Answers
Answer:
0 (option a)
Explanation:
for a number to be divisible by 5, it has to end with the digits 0 or 5. for a number to be divisible by 3, the sum of all its digits has to be divisible by 3.
for 63215: 6 + 3 + 2 + 1 + 5 = 17 (not divisible by 3)
for 63210: 6 + 3 + 2 + 1 + 0 = 12 (divisible by 3)
thus, the missing digit is 0.
i hope this helps! :D
Find the x-intercept of the line whose equation is 8x+2y=4.
1/2
4
2
Answers
Answer:
1/2
Step-by-step explanation:
8x+2y=4
To find x-intercept say y=0 and solve the equation.
8x+2(0)=4
8x=4
x=4/8
x=1/2
8x = 4
X = 1/2
3. Determine the area under the standard normal curve to the right of z = 0.55.
a.)0.2912
b.)0.7054
c.)0.7088