Answer: The correct option is (B).
True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
Step-by-step explanation:
Given that;
If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.
Lets {V₁, V₂, V₃, V₄} are linearly dependent
Then there exist a scalars C₁, C₂, C₃, C₄
So that C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0
where at least one of the Ci ≠ 0.
Take C₃ ≠ 0 then we have V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃
V₃ is a linear combination of V₁, V₂ and V₄}
that is
Given V₃ = 2V₁ + V₂
⇒ 2V₁ + V₂ - V₃ = 0
⇒ 2V₁ + V₂ + V₃ + 0V₃ = 0
Here, C₁ = 1, C₂ = 1, C₃ = -1 and C₄ = 0
So that {V₁, V₂, V₃, V₄} is linearly dependent.
therefore option B id the right answer.
- True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
B is the correct option. True, The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and the set is linearly dependent.
If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.
What is meant by linearly dependent?A set of vectors is linearly dependent if some vector can be expressed as a linear combination of the others.
Let's consider {V₁, V₂, V₃, V₄} are linearly dependent
then there exist a scalars C₁, C₂, C₃, C₄
therefore, C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0
where at least one of the Ci ≠ 0.
Lets C₃ ≠ 0 then we will get
V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃
V₃ is a linear combination of V₁, V₂, and V₄
which means V₃ = 2V₁ + V₂
2V₁ + V₂ - V₃ = 0
2V₁ + V₂ + V₃ + 0V₃ = 0
Here, C₁ = 1, C₂ = 1, C₃ = -1 and C₄ = 0
therefore, {V₁, V₂, V₃, V₄} is linearly dependent.
So, option B is correct here.
True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others, and the set is linearly dependent.
Learn more about linearly dependent here;
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30 g of pineapple are added to drink the drink rises 5 ml what is the density of the pineapple
Answer:
6g/mL
Step-by-step explanation:
Given parameters:
Mass of pineapple = 30g
Volume of rise = 5mL
Unknown:
Density of pineapple = ?
Solution:
Density of a substance is the mass per unit volume. Mathematically, it is expressed as;
Density = [tex]\frac{mass}{volume}[/tex]
The volume is the rise in the pineapple drink.
Insert the parameters and solve;
Density = [tex]\frac{30}{5}[/tex]
Density = 6g/mL
Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation.
Answer:
use the formula for a line through two points
[tex]y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \times (x - x_{1})[/tex]
plug in the given points:
[tex]y - 7 = \frac{15 - 7}{5 - 1} \times (x - 1)[/tex]
[tex]y = \frac{8}{4} \times (x - 1) + 7[/tex]
[tex]y = 2 \times (x - 1) + 7 \\ y = 2x - 2 + 7 \\ y = 2x + 5[/tex]
6570 ÷ 16
410
410 1/16
410 3/8
410 5/8
Answer:
Exact Form:
3285
8
Decimal Form:
410.625
Mixed Number Form:
410
5
8
thats what i got i hope this helps
Step-by-step explanation:
Which graph represents the linear equation y = 1?
Answer:
but there's no choices
Answer:
Since theres no options. The answer should look like this below:
<-------------------------------------------------------------------------------------------> x axis
Step-by-step explanation:
What is the following figure?
8 m
5 m
5 m
8 m
rhombus
rectangle
trapezoid
parallelogram
Answer:
rhombus
Step-by-step explanation:
you can't see what shape that is but Im doing this assignment right now I know what it looks like
Write the values of the 9s in 990.250. How are the values related?
Answer:
Leftmost 9: 900
9 between 9 and 0: 90
9 on left is worth 10 times 9 on right.
Step-by-step explanation:
990.250
The 9 at the left is in the hundreds place, so it represents 9 hundreds, so its value is 900.
The 9 between the 9 and the 0 is in the tens place, so it represents 9 tens, and its value is 90.
Since the places are right next to each other, the 9 on the left is worth 10 times the 9 on the right. Sure enough, 900 is 10 times 90.
How many millimeters are in 90 ounces?
Answer:2661615
Step-by-step explanation:
29573.5 is how many millimeters are in an ounce multiply that by 90 and you get 2661615
hope this helps
Answer:
you used two different types of things ounces measure mass and millimeters measure length
but I used google and it said 2.662e+6
the owner of an apple orchard ships apples in boxes that weigh 2 kilograms ( kg ) when empty. the average apple weighs 0.25 kg and the total weight of a box filled with apples is 12 kg. how many apples are packed in each box?
a. 14
b. 30
c. 40
d. 56
Answer: C=40
Step-by-step explanation: X=40 APPLES PER BOX.
PROOF:
2+.25*40=12
2+10=12
12=12
A large ladder leans against a house with the base of the ladder 5.8 horizontal feet from
the base of the house. If the ladder has a slope of 3.3 feet per foot, at what height does the top of the ladder meet the house? (Round your answer to two decimal places.)
=_______ft
Answer:
At 19.14 feet the top of the ladder meet the house.
Step-by-step explanation:
It is given that,
A large ladder leans against a house with the base of the ladder 5.8 horizontal feet from the base of the house.
Slope of the ladder, m = 3.3 feet/foot
We need to find at what height does the top of the ladder meet the house. Let it is h.
Base, b = 5.8 feet
It will form a right angle triangle
Slope=h/base
h = slope × base
h = 3.3 × 5.8
h = 19.14 feet
So, at 19.14 feet the top of the ladder meet the house.
The record low temperature in Pittsburgh, PA is -22°F. The record high is 103°F. What is the difference in the record high and the record low temperatures?
Answer:
The difference in the record high and the record low temperatures is 125°F
Step-by-step explanation:
Given a quantity T that varies in time, say T1 and T2, being T1 the initial value and T2 the final value.
The change or difference between the final and the initial values is:
T=T2-T1
The record low temperature in Pittsburgh, PA is T1=-22°F while its record high is T2=103°F
The difference is:
T=103°F - (-22°F)
Note both negative signs multiply to produce a positive sign, and a sum instead of a subtraction:
T=103°F + 22°F = 125°F
The difference in the record high and the record low temperatures is 125°F
find the quotient 4/7 divided by 1/5
Answer:
2 6/7
Step-by-step explanation:
You have to use the KEEP CHANGE CHANGE method. When you do this you end up with 4/7*5/1 which equals 20/7 and you then change that into a mixed number and you have your answer!
HOPE THIS HELPS!
Answer:
The answer is 2 6/7
Step-by-step explanation:
First, you set up the problem.
[tex]\frac{4}{7} / \frac{1}{5}[/tex]
Next, you change the division sign into multiplication
[tex]\frac{4}{7} x \frac{1}{5}[/tex]
Then you flip the 1/5
[tex]\frac{4}{7} x \frac{5}{1} \\[/tex]
Afterward, you multiply fractions straight across.
[tex]\frac{4}{7} x \frac{5}{1} =\frac{20}{7}[/tex]
Finally, you will simplify your answer into a mixed number.
[tex]\frac{20}{7} = 2 6/7[/tex]
Hope this helps!!
what is the product of 4/9 and 1/11? 4/99 5/99 9/44 1/4
Answer:
4/99
Step-by-step explanation:
Multiply the numerator and den0ominater, then stack them
Answer:
4/99
Step-by-step explanation:
4/9 * 1/11
Multiply the numerators
4*1 = 4
Multiply the denominators
9*11 = 99
numerator over denominator
4/99
Mrs. Lewis received her paycheck this week in the amount of $535.75. She spent $76.98 on groceries, she paid her $59.95 phone bill and she spent $22.45 at the movies. How much did she have left over?
Answer:
376.37
Step-by-step explanation:
Answer:
376.37
Step-by-step explanation:
Mr.Milton had $1200 in his savings account at the beginning of the year. If his account has a balance of $1230 at the end of the year, what percent increase of his balance?
Answer:
2.5%
Step-by-step explanation:
1230-1200 = 30
30÷1200 = 0.025
0.025 x 100 = 2.5
3 - +4 - = ?
4 4
OA.
3
7 -
4
OB.
4
3
8
OC.
8
OD. 7
WHICH ONE IS IT ?????!!!!!
Answer:
option 2 i think i hope i am right
Hey 675 m bike trails pass-through far is Meadow Aracely exhale the trail that cuts through Meadows flags meadow a measures 24 3/4m three legs measure 52.25 m on one leg measures 32 m the rest of the trail pass through forces how many meters of the trail pass through the forest
Answer:
436.75
Step-by-step explanation:
Answer:
436.75
Step-by-step explanation:
Which of the following is the solution to 17 - 2x = -11?
A. 3
B. -14
C. 14
D. -3
The answer is c because 2 times 14 is 28 and 17-28=-11
Answer:
14
Step-by-step explanation:
Divide each term by -2 and simplify
Hope this helped!
help me plz i promise i will mark brainliest
Answer:
The answer is A.
Step-by-step explanation:
<2 and <3 are ____ angles
complementary
vertical
congruent
supplementary
Answer:
I think it's supplementary
Answer:
supplementary
Step-by-step explanation:
∠2 and ∠3 are supplementary angles
this means ∠2 and ∠3 are equal to 180
Let f(x)=(5)x+12. Evaluate f(0) without using a calculator.
Answer:
f(0) = 12
Step-by-step explanation:
You want to substitute 0 for x
f(0) = 5(0) + 12
f(0) = 12
Answer:
13
Step-by-step explanation:
Substitute 0 for x and simplify. f(0)=(5)0+12=1+12=13.
is the ratio of chocolate to ice cream comes in a book is 5:8 and the number of chocolate is 30 find the number of ice cream cones
Answer:
48
Step-by-step explanation:
If you deposit $850 into an account which earns 6% yearly interest compounded monthly, how much will be in the account after 4 years, assuming you never withdraw money from the account? Round your answer to the nearest cent if necessary and do not include the dollar sign.
Answer:
1079.9
Step-by-step explanation:
A = P(1 + [tex]\frac{r}{n}[/tex])^nt
A: ending amount
P: principal (850)
r: interest rate in decimal form (.06)
n: compounding periods, 12 months in a year.
t: time in years (4)
= 850(1 + .06/12)^12(4)
= 850(1.005)⁴⁸
= 850(1.2704891)
= 1079.9157
Answer:
1079.92
Step-by-step explanation:
0.42 - 4) = 0.24 + 7)
Answer:
im sorry if not but i think its 7.24
Step-by-step explanation:
What is the domain of this function?
Domain = inputs = x = { 1 , 2 , 3 }
Range = outputs = y = { 2 , -1 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
2 pay raises in 3 years unit rate
Answer:
1:1.5
Step-by-step explanation:
cut the 3 in half and cut the 2 in half
Look at this equation.
0.3x + 5. 14 = 2. 1x - 4.4
Which value of x makes the equation true?
0
-5.3
O - 4.1
O 4.1
O 5.3
Answer:
5.3
Step-by-step explanation:
1.8x = 9.4
x = 5.3
The value of x that makes the equation true is 5.3, the correct option is D.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in determination of unknown parameters.
The equation is,
0.3x + 5. 14 = 2.1x - 4.4
The equation is made of two expressions,
The expression 1 is : 0.3x + 5. 14
The expression 2 is : 2.1x - 4.4
The value of x that makes the equation true has to be determined.
0.3x + 5. 14 = 2.1x - 4.4
Grouping the like terms on one side.
5.14 +4.4 = 2.1x -0.3x
Solving the variables and constants
9.54 = 1.8 x
Dividing 1.8 on both sides of the equation.
x = 9.54 /1.8
x = 5.3
The value of x at which the equation is true is 5.3.
To know more about Equation
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Please help me I will give you the brainliest (I Didn’t spell that right but don’t care)
Answer:
positive
positive
negative
1 or -1
Step-by-step explanation:
Answer:
The product of two positive integers is always a positive
The product of two negative integers is always a positive
The product of a positive integer and a negative integer is always negative
The product of any integer and -1 is always a 1 or -1
Step-by-step explanation:
Hope this helps :)
How do I work this problem -16f+13=2f-11
Answer:
f = 4/3
Step-by-step explanation:
-16f + 13 = 2f - 11
24 = 18f
Divide
24/18 = f
4/3 = f
[tex] - 16f + 13 = 2f - 11[/tex]
Subtract sides -13
[tex] - 16f + 13 - 13 = 2f - 11 - 13 \\ [/tex]
[tex] - 16f = 2f - 24[/tex]
Subtract sides -2f
[tex] - 16f - 2f = 2f - 2f - 24[/tex]
[tex] - 18f = - 24[/tex]
Negatives simplifies
[tex]18f = 24[/tex]
Divided sides by 18
[tex] \frac{18}{18}f = \frac{24}{18} \\ [/tex]
[tex]f = \frac{4}{3} \\ [/tex]
_________________________________
And we're done.....♥️♥️♥️♥️♥️
The ages of three siblings are all consecutive integers. The sum of their ages is 39. How old is the youngest sibling?
could anyone explain this in a 2 part answer
Answer:
Let x = the age of the youngest child
Let x + 1 = the age of the middle child
Let x + 2 = the age of the oldest child
x + x + 1 + x + 2 = 39
3x + 3 = 39
3x = 36
x = 12 years