A system of vectors v1, v2, . . . , vn in a vector space v of dimension n is linearly independent if and only if it spans v.
Let's first assume that the system of vectors v1, v2, . . . , vn in v is linearly independent. This means that none of the vectors can be written as a linear combination of the others. Since there are n vectors and v has dimension n, it follows that the system is a basis for v. Therefore, every vector in v can be written as a unique linear combination of the vectors in the system, which means that the system spans v.
Conversely, let's assume that the system of vectors v1, v2, . . . , vn in v spans v. This means that every vector in v can be written as a linear combination of the vectors in the system. Suppose that the system is linearly dependent. This means that there exists at least one vector in the system that can be written as a linear combination of the others. Without loss of generality, let's assume that vn can be written as a linear combination of v1, v2, . . . , vn-1. Since v1, v2, . . . , vn-1 span v, it follows that vn can also be written as a linear combination of these vectors. This contradicts the assumption that vn cannot be written as a linear combination of the others. Therefore, the system must be linearly independent.
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15•(13 - 7) ÷ (8 - 5) Simplify
Answer:
30
Step-by-step explanation:
15•(13-7)÷(8-5)
15•(6)÷(3)
90÷3
30
Answer:
30
Step-by-step explanation:
15 x 6 / 3 =
90 / 3 =
30
Hope that helps!
1. Use a trigonometric ratio to determine the value of x for each the
triangle. Round your answer to the nearest hundredth. *
8 mm
Х
26°
Is -3x+5=-3x+8 infinate many solutions
What are three other names for range. ( This is for algebra)
A water bottle costs $9.45. Sales tax is 7%. What is the total cost?
Answer:
$10.11
Step-by-step explanation:
Before Tax Price: $9.45
Sale Tax: 7.00% or $0.66
After Tax Price: $10.11
Answer:
9.46
Step-by-step explanation:
divide 9.45 by .07 then add that to 9.45 and round
Can anyone help me please
I’ll mark brainliest.
Answer:
1. his account will be 120
2. 6 weeks
3. Yes, Lala will get 120 in 4 weeks while Andra will get 100
If you wanted to know Andra equation will be y=20x+20
Step-by-step explanation:
Hope this helped
I need help with this
9514 1404 393
Answer:
perimeter: 20 unitsarea: 27.5 square unitsStep-by-step explanation:
We must assume the pentagon is regular. Its 5 sides are all the same length as AB, which is 4 units. So, the perimeter is ...
P = 5s = 5(4) = 20 . . . units
__
The area is given by the formula ...
A = (1/2)Pa
where P is the perimeter and a is the apothem--the distance from the center to one side.
The center coordinates are (3, 4.75), so the center is 2.75 units from side AB at y=2. Then the area is ...
A = (1/2)(20)(2.75) = 27.5 . . . square units
Which expression is represented by the model below?
2 bars are shown next to each other and each bar is labeled
A.
8
×
2
3
B.
3
×
2
8
C.
8
×
3
2
D.
2
×
3
8
Answer
its d
Step-by-step explanation:
The expression that is represented by the model below is -
y = 2 x 3/8.
What is expression in mathematics?An expression in mathematics is a combination of terms both constants and variables.
Given are two labelled bars shown next to each other and each bar.
3 of the 8 bars are colored. Using fraction, we can represent it as -
{f} = 3/8
There are two such bars, so we can write -
y = 2{f}
y = 2 x 3/8
Therefore, the expression that is represented by the model below is -
y = 2 x 3/8.
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explain the arrangements of the atoms, I already have the first part done
Step-by-step explanation:
The ongoing arrangement of metal atoms in a three-dimensional regular ordered pattern is known in chemistry as a lattice structure. A simple model of an atom is a central atomic nucleus with electrons arranged in shells at different distances from the nucleus.
help me guysssssssssssssssss :D
Answer:
Slope=3
Step-by-step explanation:
m=y2-y1/x2-x1
m=19-10/6-3
m=3
Answer: The answer is C which is "m = 3"
Step-by-step explanation: To find the slope, the formula is change of y / change of x. The change of y in the graph is 9, and the change of x is 3. 9 divided by 3 is 3. Therefore, the option "m=3" is the correct answer.
A store has apples on sale for $21.00 for 6 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $126.00? Complete the explanation.
Answer:
115 apples
Step-by-step explanation:
6 pounds of apple = $21.00
Cost per pound :
$21.00 / 6 = $3.5 per Pound
1 pound = 16 ounces
16 ounces cost $3.5
1 ounce = $3.5 / 16 = $0.21875
5 ounces will cost :
5 * 0.21875 = $1.09375
Number of 5 ounce apple that can be purchased with $126
$126 / $1.09375
= 115.2
Approximately 115 apples
Please answer for kind of a lot of points :D
Answer:
(5.5d + 8) miles27.5 milesStep-by-step explanation:
Lyndsay ⇒ 3d + 5Seth ⇒ 2.5d + 3a) Together they run:
3d + 5 + 2.5d + 3 = (5.5d + 8) milesb) They run 5 days Monday through Friday last week:
5.5*5 = 27.5 milesTwo lines A and B are parallel if both lines are rotated 90° in the same direction and then translated to the right by the same number of units which statement about the lines resulting from these transformations is true
Answer:
A' and B' will be parallel. (See Explanation)
Step-by-step explanation:
Given
Parallel lines: A and B
Rotation: 90° same direction
Translation: Right (same units)
Required
Describe the result of the transformation
No options were given. So, I will answer on general terms.
From the question, we can see that, the same transformation that was performed on line A was also done on line B.
This means that both lines will maintain the initial relationship between them.
Initially, A and B are parallel.
After the transformation, A' and B' will be parallel.
Answer:They will be the same line
Step-by-step explanation:I did this on my test it’s correct
Use the following table to find the Rate of Change.
Answer:
x=1 and y= 6
Step-by-step explanation:
and for y its a positive cause their both negitives
Find a positive angle that is less than 360° that is coterminal with a -80°
angle
*
260°
440°
-440°
None of the above
2. Jules conducted a survey and asked 100
people how many years of education they have
and what their annual income is. She used the
results to make a scatter plot.
What type of assoastion should she expect to see in the scatter plot
are the rates equivalent?
Answer:
No
Step-by-step explanation:
0.3/4= 0.075
0.9/15= 0.016
They aren't equal.
Answer:
no they are not
Step-by-step explanation:
cause I said
PLEASE HELP ME!! I will give brainliest
Answer:
D
Step-by-step explanation:
It is on the positive side of the graph and the point is on 3,1
The measures of the angles of a triangle are shown in the figure below.Solve for X.
Answer:
x=3
Step-by-step explanation:
51 degrees + (7x+18) degrees = 90 degrees
7x+18=90-51
7x+18=39
7x+18-18=39-18
7x=21
7x/7=21/7
x=3
hallar 4 números naturales pares consecutivos cuya suma sea igual a 44
Answer:
11+11+11+11=44
Do I have to use different numbers?
10+14+12+8=44
Consider the system of equations.
8x+2y=8
y= −4x+4
The system has blank solutions.
SELECT CHOICE
no,
infinitely many,
one.
then both equation r same after we re arrange it so no result
2x-6y=12 and -5x+15y=-30 elimination
Answer:
unsolvable because the second equation is just -2.5 times the first equation.
Step-by-step explanation:
2x-6y=12 then 2x=12+6y x=6+3y
-5x+15y=-30
substitute x
-5(6+3y)+15y=-30
-30-15y+15y=-30
y=y
What type of decimal is 0.275
A. Repeating Decimal
B. Terminating Decimal
C. Non-Terminating Decimal
D Complex Decimal
Answer:
Complex Decimal.
it is the correct answer.
Need help with this problem
m∈(-∞,-4)∪(4,+∞)
Step-by-step explanation: Photo Math App
Please help me -5x-3y=16 y=x
Answer:
the answer is x=2 and y=2
Step-by-step explanation:
-3y=16+5x
-y=(16+5x)3
If anyone can answer these questions that would help a lot. Besides 13 and 14
can someone please explain this
Answer:
14 cm²
Step-by-step explanation:
1/2 (7•4)
1/2 (28)
14
Answer:14
Step-by-step explanation:
I believe it is asking you to multiply 4 and 7 getting 28, then divide that by 2 so 14
Please help ASAPPPPPO
Answer:
x=all real numbers
y=all real numbers
Step-by-step explanation:
x=-5y-1
-3(-5y-1)-15y=3
15y+3-15y=3
3=3
therefore the answer is all real numbers
epic math question that i cant solve
imao help me with zearn
Answer:
4
Step-by-step explanation:
if there are 8 ounces for 2 then there are 4 ounces for 1.
Answer:
with what?
Step-by-step explanation: