The span of a set of vectors is the set of all possible linear combinations of those vectors. So, if we have vectors v1, v2, …, vm in Rn, then the span of these vectors will be the set of all possible linear combinations of these vectors. This means that any vector in the span can be expressed as a linear combination of v1, v2, …, vm.
Now, to determine whether the span of these vectors is necessarily a subspace of Rn, we need to check the three subspace axioms: closure under addition, closure under scalar multiplication, and contains the zero vector.
Closure under addition: Let u and v be two vectors in span(v1, v2, …, vm). This means that u and v can be expressed as linear combinations of v1, v2, …, vm. Therefore, their sum u + v can also be expressed as a linear combination of v1, v2, …, vm, and so u + v is also in the span. Thus, the span is closed under addition.
Closure under scalar multiplication: Let c be any scalar and let u be any vector in span(v1, v2, …, vm). This means that u can be expressed as a linear combination of v1, v2, …, vm. Therefore, cu can also be expressed as a linear combination of v1, v2, …, vm, and so cu is also in the span. Thus, the span is closed under scalar multiplication.
Contains the zero vector: Since the zero vector can always be expressed as a linear combination of the vectors v1, v2, …, vm (by taking all coefficients to be zero), it follows that the span contains the zero vector.
Therefore, since the span of v1, v2, …, vm satisfies all three subspace axioms, it is necessarily a subspace of Rn.
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Find x ( transversals relations )
Answer:
x = 12
Step-by-step explanation:
(8x - 34) and (5x + 2) are alternate angles and congruent, then
8x - 34 = 5x + 2 ( subtract 5x from both sides )
3x - 34 = 2 ( add 34 to both sides )
3x = 36 ( divide both sides by 3 )
x = 12
Three sisters have ages that are consecutive odd integers. The sum of their ages is 57. Find the age of each sister.
Answer:
The answer is 17 19 and 21
hope i could help!
PLEASEEEEEE!!! help with this
PLEASE EXPLAIN HOW TO DO THIS LIKE IN STEPS AND EVERYTHING
Explain, in detail, the steps on how to factor the following trinomial.
3x^2+5x +2
Answer:
(3x+2)(x+1)
Step-by-step explanation:
Given the quadratic equaton;
3x^2+5x +2
Factorize
(3x^2+3x+)(2x+2)
Factor out the common value from each bracket
3x(x+1) + 2(x+1)
3x+2(x+1)
Hence the factored form is (3x+2)(x+1)
Is the following triangle congruent by SAS, ASA, or SSS? Why?
Answer:
ASA
Step-by-step explanation:
As it is shown
m<A = m<Z
m<Y = m<C and
|YZ| = |AC| so the triangles are congruent by ASA
Please help
Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.
Answer:
distributive property
9x+15
Step-by-step explanation:
The distributive property is whenever you have () and distribute until you have zero of these ()
The equivalent expression simply means write this equation differently.
The price have changed from $120 to $75. By how many
percent did it change?
Plz show how you did it
Answer:
around 37%
Step-by-step explanation:
120 × (1 - 37%) = 120 × (1 - 0.37) = 75.6
if im being honest i used calculator . net's percentage calculator
What is 30% of 42?
I’ve given up on my hw pls help
Answer:
12.6 is the answer! happy to help ya :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
42(30/100)
12.6
Are these two triangles congruent? *
Answer:
not congruent because none of the angles match
Answer:
Not Congruent
Step-by-step explanation:
No.
Two corresponding sides measure 8 and 4.
The other two corresponding sides measure 7 and 3.5.
In order to be congruent, each pair of corresponding sides has to be congruent.
write a linear equation of a line that goes through (8,0) and (-6,7)
Answer:
Line equation: y=−0.5x+4
Slope: -0.5
Intercept: 4
Step-by-step explanation:
Mister Lincoln by juices and water for the school picnic a pack of their juices box cost $5 about the six water bottles cost $3 Mister Lincoln spends $94 for a Hyundai Sonata juice boxes and bottled water.
Answer:
10 packs of juice and 15 packs of water was bought by Mr. Lincoln
Step-by-step explanation:
Mr. Lincoln buys juice and water for the school picnic. A pack of 8 juice boxes costs $5. A pack of 6 water bottles costs $3. Mr. Lincoln spends $95 for 170 juice boxes and bottles of water.
Solution:
Let x represent the number of packs of juice boxes bought by Mr. Lincoln and let y represent the number of packs of water bottles bought by Mr. Lincoln.
Each pack of juice cost $5 while each pack of water cost $3. Mr. Lincoln spends $95, therefore:
5x + 3y = 95 (1)
Each pack of juice contain 8 juice boxes and each pack of water contain 6 water bottles. Since 170 juice boxes and bottles of water was bought, therefore:
8x + 6y = 170 (2)
Solving equations (1) and (2) simultaneously. Multiply equation (1) by 2 and then subtract equation (2) from the result to get:
2x = 20
x = 10
Substitute x = 10 in equation (1):
5(10) + 3y = 95
50 + 3y = 95
3y = 45
y = 15
Hence 10 packs of juice and 15 packs of water was bought by Mr. Lincoln
Which Paris of triangle must be similar?
Triangles 1 and 2 are equilateral
help pleasseeeeeeeeee
Answer:
B, C, E, F
Step-by-step explanation:
Find the number of terms in this polynomial. 7g7 + 10g4 – 6g3 + 3g2 - g
Answer:
If you have more than 4 terms you say polynomial with the certain number of terms you have. So the answer to this is polynomial with 5 terms.
Hope this helps.
What is the difference?
Answer:
I WAS WRONG PICK D
Step-by-step explanation:
I'm an idiot
Factor x⁴y² + x³y³.
A. x 3y 2(x + y)
B. x³y² (x + 1 )
C. x²y² (x + y)
Answer:
A..........,..,......
Step-by-step explanation:
....,.............
Please help meeeee!!!!!!!!! What’s the answer????
Answer:
The answer would be y= |x-2| -1.
When graphing the answer B would be a larger quantity but A is the correct answer. Hope this helps :))
I need a lot of heeelp pleaseee
Answer:
i think its mn
Step-by-step explanation:
its the 2 close to qs
Use multiplication to solve the proportion. a/6 = 15/2
Answer:
[tex]\frac{a}{6}[/tex] = [tex]\frac{15}{2}[/tex]
2a = 6 · 15
2a = 90
a = 45
Step-by-step explanation:
Suppose that $1,000 is deposited into an account that yields 0.85% interest, compounded annually.
How much money will be in that account at the end of 4 years? Round your answer to the nearest
cent
=====================================
Work Shown:
A = P*(1+r/n)^(n*t)
A = 1000*(1+0.0085/1)^(1*4)
A = 1034.43596172007
A = 1034.44
---------------------
Notes:
P = 1000 is the deposit or principalr = 0.0085 is the decimal form of the annual interest rate of 0.85%; we can say 0.85% = 0.85/100 = 0.0085n = 1 represents how many times per year we're compounding the money (ie annually)t = 4 = number of yearsThe result of 1034.44 dollars is only possible if you do not withdraw any of the money in the four year time period.please help! thank u!
Step-by-step explanation:
I cannot see the correct value so u check yourself. but this is the correct graph.
An escalator 152 feet in length rises to a platform and makes a 31° angle with the ground. Find the height of the
platform above the ground.
Answer:
78.3 or 78.29
Step-by-step explanation:
We are asked to find the height of the figure which is the vertical side of the triangle. We are given an angle and we are a side opposite of that angle( the height of the platform) and the hypotenuse 152. So we are going to use sine.
Opposite/Hypotenuse
We use this equation
[tex] \sin(theta) = \frac{opp}{hypo} [/tex]
Plug in the values
[tex] \sin(31) = \frac{x}{152} [/tex]
Which is about 78.29
Shirley went shopping in a mall. She reached the mall 12.5 minutes later than her usual time. While returning she took 20 minutes more than twice her usual time to reach home. If the usual time she takes to reach the mall is 40 minutes, find the total number of minutes Shirley spent going and coming back from the mall.
Answer:
Total time Shirley spent going and coming back from the mall= 152.5 minutes
Step-by-step explanation:
Usual time it takes to reach mall from home = 40 minutes
New time she took to reach the mall=12.5 minutes later than her usual time
= 40 minutes + 12.5 minutes= 52.5 minutes
New time she took to reach home ( lets assume she followed the same route as coming from home in which she spends 40 minutes) =20 minutes more than twice her usual time to reach home.=20 minutes + 2(40)= 20 minutes + 80 minutes
=100 minutes
Total time going and coming back from the mall =52.5 minutes +100 minutes = 152.5 minutes
If the sumof two numbers is 4 and the sum of their squarea minus three times their product is 76, find the two numbers
Answer:
Step-by-step explanation:
If the sumof two numbers is 4 and the sum of their squarea minus three times their product is 76, find the two numbers
Let us represent:.
First number = x
Second number = y
If the sum of two numbers is 4
= x + y = 4
x = 4 - y
The sum of their squares minus three times their product is 76
x² + y² - 3xy = 76
We substitute 4- y for x
(4 - y)² + y² - 3(4 - y)y = 76
(4 - y)(4 - y) + y² - (12 - 3y)y = 76
16 - 4y - 4y - y² + y² - 12y - 3y² = 76
16 -20y - 3y² = 76
3y² + 20y - 16 + 76 = 0
3y² + 20y + 60 = 0
what's the value of
[tex](2 \sqrt{2}) {}^{2} [/tex]
chess ?
Answer:
jbtcxey5x6ivb
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
(2√2)^2
= (2^2× √2^2)
=(4×2)
=8
If you borrow $491 for one year at an interest rate of 9%, how much interest will you pay?
Answer:
44.19
Step-by-step explanation:
419*0.09=44.19
Challenge. A large university accepts 60% of the students who apply. Of the students the university accepts, 50% actually enroll. If 10,000 students apply, how many actually enroll?
Answer: 3,000
Step-by-step explanation:
Apply= 10,000
University Accept= 10,000*60% = 6,000
Enroll= 6,000*50% = 3,000
Write as an addition problem: 22 - (-8)
Step-by-step explanation:
22+8
I think this ans may help you
Quincy has box of cereal to eat over 6 days. If he splits the box into equal portions, how much will he eat each day?
Answer:
1/6 of the cereal box
Step-by-step explanation:
Could someone Please Help me with this?!?!?!?!
Answer:
-3
Step-by-step explanation:
To find slope use the equation [tex]y2 - y1 / x2 - x1[/tex]
1. Pick any two coordinate pairs to use in the equation. I'll choose (-2, 7) and (-1, 4).
2. Plug these coordinates into the formula. 4 - 7 / -1 - - 2
3. Solve! -3/ 1 = -3
4. The slope of this line is -3
The table shows two linear functions and the function values for different values of x.
Which expression represents h(x)?
A. (f ∙ g)(x)
B. (g + f)(x)
C. (f – g)(x)
D. (g – f)(x)
Answer:
the answer is A. (f ∙ g)(x)
Step-by-step explanation:
i got it wrong twice, and then it told me the answer
Answer:
its A
Step-by-step sussy vent imposter baka :) ;0