The set s consisting of pairwise orthogonal non-zero vectors in Rn is linearly independent.
How to prove set is linearly independent?To prove that the set s is linearly independent, we need to show that the only solution to the equation:
c1v1 + c2v2 + ... + cnvn = 0
is the trivial solution c1 = c2 = ... = cn = 0.
Suppose there exists a non-trivial solution to the above equation, i.e., there exists some non-zero vector c = (c1, c2, ..., cn) such that:
c1v1 + c2v2 + ... + cnvn = 0
Then, taking the dot product of both sides with vi, we get:
(ci vi)· vi = 0
since the dot product of any two orthogonal vectors is zero.
Thus, we have:
civi · vi = 0
or
civi² = 0
since vi·vi = ||vi||² ≠ 0, as each vector is nonzero.
Since each vector in s is nonzero, this implies that ci = 0 for all i, since the square of any nonzero scalar is nonzero. Therefore, the only solution to the equation c1v1 + c2v2 + ... + cnvn = 0 is the trivial solution c1 = c2 = ... = cn = 0.
Thus, the set s is linearly independent
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The graph of a linear function is often a parabola.
True or False
A linear function has a graph as a straight line so the given statement is False.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear function is given by
y = mx + c where m is the slope and constant.
Since it is constant it means it should be a straight line in coordinate geometry.
Therefore a linear function always makes a straight line, not a parabola.
Hence "A linear function has a graph as a straight line so the given statement is False".
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Perform the indicated operation.
f (x) = x2 − 1 g(x) = 3x + 4 Find f (9) − g(9)
Answer:
f(9)=17//g(9)=31
Step-by-step explanation:
substitute- (9)2-1= 18-1=17
substitute and solve- 3(9)+4=27+4=31
Hope this helps
Translate X(2,3) Y(0,0) Z(4,4) 2 units right and 3 units up
Answer:
X(4, 6) Y(2, 3) Z(6, 7)
Step-by-step explanation:
If you want to translate something right on a number line, then you are essentially adding to it. Thus you would just add 2 to each of the x values of the coordinates. The same applies with translating something up, all that really means is that you are adding to each of the y values so all you have to do is add 3 to each of the y values and you get your answer.
Answer:
X:(4,6), Y:(2,3), Z:(6,7)
Step-by-step explanation:
2 units right implies a change on the x-axis, meaning you add 2 units to the x of the coordinate pair (x, y). 3 units up implies a change in Y, you apply the same rule and add 3 to the Y of the pair.
2 units right (add 2 to x pair coordinate)
X: (2,3) --> (4,3)
Y: (0,0) --> (2,0)
Z:(4,4) --> (6,4)
and 3 units up (add 3 to y pair coordinate)
X: (4,3) --> (4,6)
Y: (2,0) --> (2,3)
Z: (6,4) --> (6,7)
En un almacén de dimensiones 5m de largo ,3m de ancho y 2m de alto queremos almacenar cajas de dimensiones 10 dm de largo 6dm de ancho y 4 dm de alto ¿cuántas cajas podremos almacenar?
Answer:
how do you translate
Step-by-step explanation:
The face of a clock has a circumference of 14π inches. What is its area?
Answer:
A = 49π
Step-by-step explanation:
C = πd
if d = 14 then r = 7
A = πr²
A = π · 7²
A = 49π
15% of 130 using the decimal method
Answer:
0.3846 is a decimal and 38.46/100 or 38.46%is the percentage for 50/130
Step-by-step explanation:
Pls mark me in brain list
Answer:
0.3846 is a decimal and 38.46/100 or 38.46%is the percentage for 50/130
Step-by-step explanation:
POR QUE ES IMPORTANTE LA GEOMETRIA EN NUESTRA VIDA
Step-by-step explanation:
La geometría permite a los estudiantes conectar objetos cartográficos en el aula con contextos del mundo real con respecto a la dirección y el lugar. La comprensión de las relaciones espaciales también se considera importante en el papel de la resolución de problemas y las habilidades de pensamiento de orden superior.
Totally out of points
Need triangle geom help !
Answer:
B. ∠BAC
Step-by-step explanation:
The angle opposite the largest side has the largest angle.
What is the length of the diagonal of a 10 cm by 15 cm rectangle
Answer:
5 root 13
Step-by-step explanation:
using the pytogorean therom we get
root(10 squared +15 squared)
=root(100+225)
=root(325)
=5 root 13
pleade help and show work
9514 1404 393
Answer:
11) x = 9
12) x = 9
Step-by-step explanation:
11) Corresponding segments are proportional, so ...
x/6 = 12/8
x = 6(12)/8 . . . multiply by 6
x = 9
__
12) Similar triangle relationships show you the geometric mean relationship that applies in this case.
long side/short side = x/3 = 27/x
x² = 3·27 . . . . . . cross multiply
x = √(3·27) . . . . geometric mean relationship
x = 9
Someone plz help me with this question with an explanation
To use the angle-angle similarity theorem you need to know 2 corresponding angles of each triangle are the same.
You are already shown that angles H and M are the same.
The sets of corresponding angles are:
H and M, N and I, and O and J
The answer would be angle O and angle J are similar.
Salesman Scott received $2,792.79 for selling a property. If the gross commission was 6.5 % of the sale price, the listing salesman received 12% of the gross commission and Scott received 45% of the balance, how much did the property sell for?
Answer: The property sold for $5,870.41.
Step-by-step explanation:
Let x be the selling price of the property.
Then, gross commission = 6.5% of x = 0.065x
listing salesman received = 12% of ( 0.065x) = 0.12 (0.065x) = 0.0078 x
Balance = x - ( 0.065x) - (0.0078 x)
= (1+0.065-0.0078)x
= 1.0572x
Scott received = 45% of (1.0572x)
=0.45 (1.0572x)
= 0.47574x
Now, [tex]0.47574x=2,792.79[/tex]
[tex]\Rightarrow\ x=\dfrac{2792.79}{0.47574}\\\\\Rightarrow\ x=5870.41[/tex]
Hence, the property sold for $5,870.41.
given teach trig ratio as a fraction in simplest form:sin(N)
Answer:
Choice #1: sq rt 3/2
Step-by-step explanation:
cos N=8/PN
PN=16
tan N=PO/8
PO=13.86
sin N=13.86/16=0.866=sq rt 3/2
brainliest to whoever can answer questions correctly
Answer:
v ~ 32.72
Hope that helps!
Raj is thinking of a fraction that is equivalent to 5/8 in which the numerator is greater than 20 and the denominator is less than 50. What is the fraction Raj is thinking about?
Answer:
25/40
Step-by-step explanation:
5 into 8 is 40 and 5 into 5 is 25
Answer:
20 / 32
but the numerator is equal to 20, not greater than 20.
Step-by-step explanation:
5/8 = 10/16 = 20 / 32
Estelle's graduation picnic will cost $15 if it has 5 attendees. If there are 26 attendees, how much will Estelle's graduation picnic cost? Solve using unit rates.
Answer:
You can try to do a direct rule of three in this exercise.
We can considerr that the relation is proportional and we know that in this case it's dorect, as the more attendees there come, the more Estelle will have to pay, so we can write this and get x:
5 attendees - 15 dollars
26 attendees - x dollars
x = 26*15 / 5 = 78 dollars
So you know how much Estelle would have to pay
The cost c to rent a car for d days is shown in the
table. Which equation represents this function?
Answer:
i would help you but there is no table so, sorryStep-by-step explanation:
am goblin gimme ye pointswhich number is composite? 11,2,9,5
Answer:
Answer is 9.
Step-by-step explanation:
Composite number is 9.
I hope it's helpful!
27 of the 180 vehicles in a movie theater parking lot are minivans.What percent of the vehicles in the parking lot are minivans?
Answer:
160
Step-by-step explanation:
Answer:
15 percent
Step-by-step explanation:
First use the equation part over total to get 27/180. Then reduce the equation by dividing both the numerator 27 and the denominator 180 by 9. You are left with 3/20. Then use your calculator or you can work it out long hand to get 0.15. You times 0.15 by 100 if you want to find the percent, leaving you with 15 percent.
I hope this helped! :)
Given the function f(x) graphed on the coordinate plane 15
below, determine f(3).
F(3)= ?
Answer:
2
Step-by-step explanation:
how to factorise
25x²- 64y²
Answer:
(5x + 8y)(5x - 8y)
Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula, a^2 - b^2 = (a + b)(a - b) where a = 5x and b = 8y.
~Hoped this helped~
for what value of m is equivalent to..
Answer:
A
Step-by-step explanation:
because math
I need help on this please:)
Answer:
Step-by-step explanation:
∠x=180-114
=66°
∠p=114 (alt.ext.∠)
Answer:
Although it is not stated... I am assuming line "m" and line "n" are parallel to each other. That's the only way we can solve the problem..
Write a ratio for the following situation. For every 10 toes, there are 2 feet.
Answer:
5:1
Step-by-step explanation:
10 toes = 2 feet
10:2
Simplify!
5:1
Helllllllp
Simplify the expression 43 + 2(3 − 2).
14
16
66
68
Answer:
68
Step-by-step explanation:
Answer:
The answer is 46...i cant find that answer in the choices though
Step-by-step explanation:
In PEMDAS we can see that we have parentheses first so we solve whatever is in the parentheses. which 3-2 = 1....so it should look like this
43 + 2 + 1
Which equals 46
hope this helps. have a good day
Distribute Terms
-5(x +2)
-5x-10
hope that helps^^
y = 2x + 7
y=2X+7
O one solution
O two solutions
O no solution
O infinitely many solutions
Answer:
Infinitely many solutions
Step-by-step explanation:
The lines overlap one another and this leads to an infinite amount of solutions.
Answer:
one solution is the answer
tan^2 30 +tan ^2 45+tan^2 60
Step-by-step explanation:
tan 30 = 1/√3tan 45 = 1tan 60 = √3 = tan² 30 + tan² 45 + tan² 60 = ( 1 /√3 )² + ( 1 )² + ( √3 )² = ( 1 / 3 ) + ( 1 ) + ( 3 ) = ( 1 + 3 + 9 ) ÷ 3 = 13 ÷ 3 = 4.333MARK ME AS BRAINLISTIn the rhombus,
mZ1 =15x, mZ2 = x+y, and m/3 =9z.
Find the value of each variable. The diagram
is not to scale.
2 | 1
a. x = 12, y = 84, z = 20
b. x = 6, y = 174, z = 20
c. X= 6, y = 84, z = 10
d. x = 12, y = 174, z = 10
For the M1 angle, we can conclude the size of angle is 90°. Do the angle equation like this :
15x=90
x = 90/15
x = 6
Do the same thing in M2 :
Subtitute the x value to equation, then evaluate the value by using 90 because it's the same.
x+y=90
6+y=90
y=90-6
y=84
M3 value is same, 90°
9z=90
9z/9 = 90/9
z=10
Hope this helps
3x - 5 = -3 is the answer positive or negative
Answer:
positive
Step-by-step explanation:
if you time the three by a postive then times that by a negetive you get a negitive if you time by two negitives you get postive
In the expression 3x - 5 = - 3 the value of x is positive 2/3.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 3x - 5 = - 3.
3x = - 3 + 5.
3x = 2.
x = 2/3 so x is positive.
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