Prove or disprove that the vector V1=(1,2,3) v2=(1,1,1) and V3=(1,1,0) are linearly indepwndent in vector space R^2?

Answers

Answer 1

Answer:

The equations are linearly independent in vector space R²

Step-by-step explanation:

The given vectors are;

V₁ = (1, 2, 3), V₂ = (1, 1, 1), V₃ = (1, 1, 0)

For the vectors to be linearly dependent, we have;

a₁·V₁ + a₂·V₂ + a₃·V₃ = 0

Where;

a₁, a₂, and a₃ are not all zero

We get;

[tex]\left[\begin{array}{ccc}1&2&3\\1&1&1\\1&1&0\end{array} \right][/tex]

The vectors are linear dependent, if the following system of equation has a unique set of solution

x + y + z = 0...(1)

2·x + y + z = 0...(2)

3·x + y = 0...(3)

From equation (1), we have;

x = -(y + z)

∴ y + z = -x

Plugging in the value of y + z in equation (2) gives;

2·x + y + z = 0

2·x + y + z = 2·x - x = x = 0

x = 0

From equation (3), we get;

3·x + y = 0, where x = 0, therefore;

3 × 0 + y = 0

∴ y = 0

From equation (1), we have;

x + y + z = 0

Where, x = 0, and y = 0, we get;

0 + 0 + z = 0

z = 0

The vectors, V₁, V₂, and V₃ are linear independent in R³

In two dimensional space, we have

x + y = 0...(1)

2·x + y = 0...(2)

x + y = 0...(3)

Subtracting equation (1) from equation (2) gives;

2·x + y - (x + y) = 2·x - x + y - y = x = 0

∴ x = 0

From equation (1), we get

x + y = 0

∴ 0 + y = 0

∴ y = 0

Therefore, the equations are also linearly independent in vector space R²


Related Questions

3. If a + b = C, which of the following statements is true?

Answers

Answer:

first one

Step-by-step explanation:

a + b = c

subtract a from both sides

b = c - a

or

c - a = b

[tex]\longrightarrow{\green{ a. \: c - a = b }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]a + b = c[/tex]

[tex]⇢ b = c - a[/tex]

[tex]⇢ c - a = b[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Math help please show work thanks

Answers

8*3=24 8*3=24 5*3=15 5*3=15 5*8=40 5*8=40
24+24+15+15+40+40
48+30+80
78+80
158
Answer:  158 square feet

=====================================================

Work Shown:

36 inches = 3 feet

Divide by 12 to go from inches to feet

The block has the dimensions

L = 5 ftW = 8 ftH = 3 ft

Use the formula below to calculate the surface area

SA = 2*(LW+LH+WH)

SA = 2*(5*8+5*3+8*3)

SA = 2*(40+15+24)

SA = 2*(79)

SA = 158 square feet

So if you had 158 square feet of wrapping paper, then you can cover this entire 3D box without any gaps or overlaps. The paper can be folded over the box, or you can cut/glue the pieces on, but make sure there isn't any leftover scraps of paper.

A shop-keeper wants to charge 1.5 times
as much per toilet roll for offer B than offer A.
What is the price for offer B?

Answers

Answer:

ok so the equation would look like this

B=1.5A

so b is 1.5 times more then a

B=1.5A So your answer is that it’s 1.5 times greater

Type the correct answer in each box. Use numerals instead of words, Simplify the following polynomial expression. (5x2 + 13x – 4) – (17x2 + 7x – 19) + (5x – 7)(3+ + 1)
____ x2 – ____ x + ____​

Answers

Answer:

La primera es la respuesta la segunda parte es la

Step-by-step explanation:

La que te muestra como va el procedimiento

Answer:

-57x^2-10x+8

Step-by-step explanation:

i just did the test on edmentum

What is the area of this tile?
Use inch or inch^2 for this problem.

Answers

Answer:

24 in^2

Step-by-step explanation:

To get the area of a triangle, multiply the base and height, then divide by 2.

Base=6

Height=8

6*8/2=48/2=24

24 in^2

Answer:

24 inch^2

Step-by-step explanation:

6 times 8 equals 48

Divide that by 2 and get 24

Area of Triangle is A=1/2bh

Can I get Brainliest, please!

Helpppppppppppp meeeeeeeeee

Answers

Answer:

X=-1

Step-by-step explanation:

X=-1 is just a vertical line since it only tells where the x point is.

Shantelle wants to rent a midsize car for one day.Value rent a car charges $20 a day plus 0.20 per mile,and best rent a car charges $30 a day plus $0.10 per mile for rental of the same mid-size car

Part A)write an equation in slope intercept form,y=mx+b for each car

Part b: determine the mileage where the rental charges are the same.

(Need help asap)

Answers

Answer:

See answers to parts a and b below.

Step-by-step explanation:

A. Value: y=20+.20x

Best Rent y=30+.10x

B. 20+.20x=30+.10x make equations equal each other by subbing y values.

.10x=10 simplify equation

x=100

check answers by subbing 100 for x in each equation.

y=20+.20(100)

y=20+20

y=40

y=30+.10(100)

y=30+10

y=40

Both equations equal 40, so 100 is the correct number of miles for when Value equals Best Rent.

Please help i don't have enough time!! PISA: Exchange rate Mei-ling from Singapore has been preparing to go to South Africa for 3 months as an exchange student. She needed to convert some Singapore dollars (SGD) into South African Rand (ZAR). Mei-Ling discovered that the exchange rate between Singapore Dollar and South African Rand SeM 1 SGD = 4.2 ZAR Mei-Ling changed 3000 Singapore Dollars to South African Rand at this exchange rate. How much money did Mai Ling get in South African Rand?

Answers

Answer:

12600 (ZAR)

Step-by-step explanation:

4.2*3000

Please help me on this!! 11 points!!!

Answers

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]

SIMPLIFY THE EXPRESSION [tex] \blue{\frac{m^{ \frac{2}{3} } }{m {}^{ \frac{1}{5} } } }[/tex]

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex] \pink{ \frac{m^{ \frac{2}{3} } }{m {}^{ \frac{1}{5} } }} \\ m^{ \frac{2}{3} - \frac{1}{5} } \\ m^{ \frac{(2 \times 5) - (1 \times 3)}{3 \times 5} } \\ m^{ \frac{10 - 3}{15} } \\ m^{ \frac{7}{15} } [/tex]

[tex] \green{SECOND \: \: OPTION->}\purple{ m^{ \frac{7}{15} } }[/tex]

Please help meee I need this done ASAP

Answers

Answer:

4pi/15=θ  - i think

Step-by-step explanation:

S = r*θ

r=9

s=12pi/5

12pi/5=9*θ

12pi/45=θ

4pi/15=θ

se
4 Shonda is hanging pictures on a
wall in her home. She has pictures
with areas of 16 square inches and
25 square inches. She hangs a total
of 7 pictures which covers 148
square inches of wall space. Let x be
the number of pictures with an area
of 16 square inches and y be the
number of pictures with an area of
25 square inches.

Answers

X+y=7 and 16x+25y=148

Fill in the blank with <,> or = . 11.01-----11.001

Answers

Answer:  Greater than sign

In other words, 11.01 > 11.001

========================================================

Explanation:

For each given number, move the decimal point 3 spots to the right.

The value 11.01 becomes 11010

The value 11.001 becomes 11001

Since 11010 > 11001, this means 11.01 > 11.001

---------------

As an alternative method, you can subtract the values to see which is larger

The rule or idea is that

(large) - (small) = positive(small) - (large) = negative

For example, 5-2 = 3 showing that 5 is larger than 2. As another example, 7-9 = -2 meaning 7 is smaller than 9. The order of subtraction matters.

In this case, 11.01 - 11.001 = 0.009 showing that 11.01 is larger than 11.001

its the last one:) please help. giving brainlist

Answers

Answer:

[tex]5[/tex]

Step-by-step explanation:

Segments are named by their endpoints. Therefore, segment PQ will have endpoints P and Q. The length of the segment is equal to the distance between these points.

To find the distance between P and Q given their coordinates, use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let:

[tex]P(-2, 7)\implies (x_1, y_1),\\Q(1, 3)\implies (x_2, y_2)[/tex]

The distance between these points is equal to:

[tex]d=\sqrt{(1-(-2))^2+(3-7)^2},\\d=\sqrt{3^2+(-4)^2},\\d=\sqrt{9+16},\\d=\sqrt{25},\\d=\boxed{5}[/tex]

Answer:

[tex]5[/tex]

Step-by-step explanation:

This problem gives one the following points on a line: ([tex]P(-2,7)[/tex]), and ([tex]Q(1,3)[/tex]). The problem asks one to find the distance between the two points. The formula to find the distance between two points on a coordinate point is the following,

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the given values in and solve for the distance;

[tex]D=\sqrt{(-2)-(1))^2+((7)-(3))^2}[/tex]

Simplify,

[tex]D=\sqrt{(-2)-(1))^2+((7)-(3))^2}\\\\D=\sqrt{(-3)^2+(4)^2}\\\\D=\sqrt{9+16}\\\\D=\sqrt{25}\\\\D = 5[/tex]

Help ASAP please thank u

Answers

Answer:

(A). F(x) = (x+1)^2

Step-by-step explanation:

If you replace x with the values of the axis, you get all the coordinates of the graph.

If this helps you, please give brainliest!

The answer is A)

Because you should horizontal shift 1 point to the left and I think the graph should parabola, so yeah hope that answers your question and good luck!!

A regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6
inches.

Approximately how many square centimeters of sheet metal will be left over as
scraps?
A. 32.9 square centimeters
B. 93.5 square centimeters
C. 113.1 square centimeters
D. 126.2 square centimeters

Answers

The correct answer to your problem would be “d”

KoKo Chocolatiers sells their truffes in rectangular boxes. They are going to start ordering circular boxes, too. The rectangular box is made from metal that is 0.3 cm thick. The circular box will be constructed from laminated cardboard that is 0.2 cm thick. The height of the circular box will be the same as the rectangular box. If the volumes of the two boxes are equal, then what is the radius (r) of the circular box?

Answers

Answer:

r = 9.61 cm

Step-by-step explanation:

Volume of a rectangular box = length × width × height

= 21.5 cm × 13.5 cm × 6 cm

= 1,741.5 cm³

Volume of a rectangular box = 1,741.5 cm³

Since,

Volume of a rectangular box = Volume of a circular box

Then,

1,741.5 cm³ = Volume of a circular box

Volume of a circular box = πr²h

1,741.5 cm³ = 3.14 * r² * 6 cm

1,741.5 = 18.84r²

r² = 1,741.5/18.84

r² = 92.436305732484

r = √92.436305732484

r = 9.6143801533163

Approximately,

r = 9.61 cm

can someone help please

Answers

9514 1404 393

Answer:

  4.  n = 4

  5.  P(A|B) = 0.75

Step-by-step explanation:

4. The coefficient of x will depend on n. The expansion is ...

  (5 +nx)^2(1 +3/5x)^n = (25 +10nx +n^2·x^2)(1 +3/5nx +...)

So, the x-term of the expansion is ...

  25(3/5nx) +(10nx)(1) = 25nx

The problem statement tells us that is 100x, so we have ...

  25nx = 100x

  n = 100x/(25x) = 4 . . . . . divide by the coefficient of n

The value of n is 4.

__

5. For the conditional probability formula, we need to know P(A∩B).

  P(A∩B) = P(A) +P(B) -P(A∪B)

  P(A∩B) = 0.5 +0.4 -0.6 = 0.3

Then the conditional probability is ...

  P(A|B) = P(A∩B)/P(B) = 0.3/0.4

  P(A|B) = 0.75

In a recent flu epidemic, the number of flu cases increased by 40% each week. There were 3,000 flu cases during the first week of January. How many more people were affected by the flu during the third week of January than during the first week?
1,200
2,880
3,280
4,200

Answers

Answer:

Option B  

(B) 2880   Hope this helps <3

Step-by-step explanation: the total number of people affected by flu during  

the 2nd and 3rd week of January, 1200 + 1680  = 2880

Answer:

1,200

Step-by-step explanation:

40%=.4

(3,000)x(.4)=1,200

1,200 more people were more affected in the third week then the first week

the koala bear is 21 inches tall. the elephant is 9 times as tall as the koala. How tall is the elephant?

Answers

9 times 21 is 189
the answer is 189 inches

Answer:

189 inches tall

Step-by-step explanation:

please help :DDDDDDD

Answers

Answer:

B 5/6 * -11/-7

Step-by-step explanation:

-5 / -7 = 5/7

-11/-6 = 11/6

Multiply

5/7 * 11/6

Rewriting

5/6 * 11/7

We can make  the 11 and the 7 negative (-11/ -7 = 11/7)

5/6 * -11/-7

Determine the measure of CD from the diagram below.

Answers

Answer:

100 degrees

Step-by-step explanation:

This is because AED And CED ARE supplimetary.

80+<CED=180

-80           -80

<Ced=100

Help please!! Worth 14 points!

Answers

Answer:

6 days

Step-by-step explanation:

Hi there!

Let d be equal to the number of days that pass.

1) Form expressions

We're told that our sister earns $30 a day, but needs to pay $60 at first:

[tex]30d-60[/tex]

We're also told that we earn $20 a day:

[tex]20d[/tex]

2) Form an equation

We're solving for the number of days that pass (d) in order for both our and our sister's income to equal each other.

For our income and our sister's income to equal each other, the following must be true:

[tex]30d-60=20d[/tex]

Because the only variable here is d, we can simply isolate it to determine the number of days that would pass.

3) Solve for d

[tex]30d-60=20d[/tex]

Subtract 30d from both sides to isolate d on one side

[tex]30d-60-30d=20d-30d\\-60=-10d[/tex]

Divide both sides by -10 to isolate d

[tex]6=d[/tex]

Therefore, for both our income and our sister's income to become equal, 6 days would pass.

I hope this helps!

If P is the incenter of JKL, find m Please show the work, that would be really helpful, thank you!

Answers

Answer:

[tex]34^{\circ}[/tex]

Step-by-step explanation:

The incenter of a triangle can be defined as the intersection of three angle bisectors that bisect all angles of the triangle.

By definition, an angle bisector divides an angle into two equal smaller angles.

Therefore:

[tex]\angle KJN=\angle LJN,\\\angle KLM=\angle JLM, \\\angle JKP=\angke LKP[/tex]

What we're given:

[tex]\angle KJN=\angle LJN=30^{\circ}[/tex] [tex]\angle KLM=\angle JLM=26^{\circ}[/tex]

The sum of the interior angles of a triangle always add up to be 180 degrees. Since these six angles make up the total sum of the interior angles, we have the following equation:

[tex]\angle KJN+\angle LJN+\angle KLM +\angle KLM +\angle JKP+ \angle LKP=180^{\circ}[/tex]

Substituting given values:

[tex]30+30+26+26+\angle JKP+\angle LKP=180[/tex]

Since [tex]\angle JKP=\angle LKP[/tex],

[tex]30+30+26+26+2(\angle JKP)=180,\\112+2(\angle JKP)=180,\\2(\angle JKP)=180-112,\\2(\angle JKP)=68,\\\angle JKP=\frac{68}{2}=\boxed{34^{\circ}}[/tex]

What is the growth factor associated with the following growth rate: 30% decrease

Your answer should be typed as a decimal.

Answers

Given:

Growth rate = 30% decrease

To find:

The growth factor associated with the given growth rate.

Solution:

The general exponential function is:

[tex]y=a(1+r)^x[/tex]

[tex]y=a(b)^x[/tex]

Where, a is the initial value, r is the growth rate in decimal and [tex]b=1+r[/tex] is the growth factor.

It is given that the growth rate is 30% decrease. So,

[tex]r=-30\%[/tex]

[tex]r=-\dfrac{30}{100}[/tex]

[tex]r=-0.3[/tex]

Now,

[tex]b=1+r[/tex]

[tex]b=1+(-0.3)[/tex]

[tex]b=1-0.3[/tex]

[tex]b=0.7[/tex]

Therefore, the growth factor is 0.7.

helppppp- u just need to simplify the given term

Answers

The answer is 8.25 or 8 1/4

I hope this helps <3

In a right triangle, Sin (4x + 10) º = Cos (6x) º. What is the value of x?

Answers

Answer:

Step-by-step explanation:

These angles will be equal when each of them measures 45 degrees. On the unit circle, 45 degrees and reference angles of 45 degrees are the only places where sin and cos are the same. This means that

sin(4x + 10) = 45 and cos(6x) = 45

If we add the angles together (the angles being 4x+10 and 6x) we get a 90 degree angle. Thus,

4x + 10 + 6x = 90 and

10x = 80 so

x = 8. Let's try it out:

sin(4(8) + 10) = sin(42) = .6691306064 and

cos(6(8)) = cos(48) = .6691306064

Yay!!!!!

The price of an item has been reduced by $1.84. The original price was $46.91. What is the price now?

Answers

Answer:

$45.07

Step-by-step explanation:

46.91-1.84= 45.07

what are the two greatest common factors in 28 and 10

Answers

1 and 2 are the greatest common factors

In the cafeteria tables are arranged in groups of 4, with each table seating 8 students. How many students can sit at 10 groups of tables?

Answers

4 tables = 1 group. So in 10 groups of tables, there are 40 tables. Each table seats 8 students, so you multiply 8 by 40, and that leaves your answer as 320 students. :)

A box of Lucky Charms costs $3.29 and you have a coupon that will save you 75 cents off 2 containers. What is the final price if you buy 2?​

Answers

The final price of the lucky charms is $2.54
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