Basis for S is B = {(1, 0, 0), (0, 1, -1)} and the dimension of S, which is the number of vectors in the basis B, is 2.
To find a basis for the subspace S, we need to determine a set of linearly independent vectors that span S. Since each row of the matrix A in M3x3(R) sums to 0, we can express this condition as a system of linear equations.
Let's denote the matrix A as:
A = [a11 a12 a13]
[a21 a22 a23]
[a31 a32 a33]
The condition that each row sums to 0 can be expressed as:
a11 + a12 + a13 = 0
a21 + a22 + a23 = 0
a31 + a32 + a33 = 0
We can rewrite this system of equations in matrix form as:
[A] * [1]
[1]
[1] = 0
where [1] represents a column vector of 1s. Notice that the right-hand side is a zero vector, indicating that the sum of each row should be zero.
To find the basis for S, we need to find the solutions to this homogeneous system of equations. We can set up the augmented matrix as:
[A | 0]
and then perform row operations to reduce it to row-echelon form. Let's proceed with the calculation:
[A | 0] = [a11 a12 a13 | 0]
[a21 a22 a23 | 0]
[a31 a32 a33 | 0]
Performing row operations:
R2 = R2 - R1
R3 = R3 - R1
[A | 0] = [a11 a12 a13 | 0]
[a21-a11 a22-a12 a23-a13 | 0]
[a31-a11 a32-a12 a33-a13 | 0]
Next, we perform row operations to eliminate the a21, a31 terms:
R3 = R3 - R2
[A | 0] = [a11 a12 a13 | 0]
[a21-a11 a22-a12 a23-a13 | 0]
[a31-a11-a21 a32-a12-a22 a33-a13-a23 | 0]
Finally, we can simplify the augmented matrix further:
[A | 0] = [a11 a12 a13 | 0]
[0 a22-a12 a23-a13 | 0]
[0 0 a33-a13-a23 | 0]
From the row-echelon form, we can see that the first column (a11, 0, 0) is a basic column. Similarly, the second column (a12, a22-a12, 0) is also a basic column. However, the third column (a13, a23-a13, a33-a13-a23) is a free column since it contains a leading 1 and zeros in its corresponding rows.
Therefore, a basis for the subspace S consists of the basic columns of the row-echelon form:
B = {(1, 0, 0), (0, 1, -1)}
The dimension of S, which is the number of vectors in the basis B, is 2.
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18+2 =20
Because 18 is 2 numbers away from 20
Answer:
Yes, that is correct.
Step-by-step explanation:
Hi! i need help asap!!
Answer:
4. 3/5
5. 1/12
6. 5/12
hope this helps
good day mate
helpppp pleaseee????
Answer:
6.68 cm radius
Step-by-step explanation:
Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178more cans than Shane did.
Write an inequality to determine the number of cans, S, that Shane could have collected.
Answer:
[911,∞)
Step-by-step explanation:
Given: S be the number of cans collected by Shane.
Since, Abha collected 178 more cans than Shane did.
Then, the number of cans collected by Abha = S+178
Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.
So,
Hence, the solution set of the inequality will be [911,∞)
Give the general solution of the linear system x+y-2z = 0 2x + 2y - 3z = 1 3x + 3y +z = 7.
The general solution to the given linear system is x = 2t - 1, y = -t + 1, and z = t, where t represents any real number.
To find the general solution to the linear system, we can use the method of Gaussian elimination or matrix operations. Let's perform Gaussian elimination to solve this system.
First, let's write the augmented matrix for the system:
[1 1 -2 | 0]
[2 2 -3 | 1]
[3 3 1 | 7]
Using row operations, we can transform this matrix into row-echelon form:
[1 1 -2 | 0]
[0 0 1 | 1]
[0 0 0 | 0]
From this row-echelon form, we can deduce that the system is consistent and has infinitely many solutions.
To find the general solution, we can express the variables in terms of a parameter, let's say t. From the row-echelon form, we can see that z = t. Substituting this into the second equation, we find that 0t = 1, which is not possible. This indicates that the system is inconsistent. However, if we ignore the last equation and continue, we can express x and y in terms of t.
From the first equation, we have x + y - 2z = 0, substituting z = t, we get x + y - 2t = 0. Rearranging, we have x = 2t - 1 - y. This implies that x depends on y and t.
Similarly, from the second equation, we have 2x + 2y - 3z = 1, substituting z = t, we get 2x + 2y - 3t = 1. Rearranging, we have y = -t + 1 - x. This implies that y depends on x and t.
Therefore, the general solution to the given linear system is x = 2t - 1, y = -t + 1, and z = t, where t represents any real number.
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True/False: let a be square real matrix if v is an eigenvector for eigenvalue λ then v is an eigenvector for eigenvalue λ
True. et a be square real matrix if v is an eigenvector for eigenvalue λ then v is an eigenvector for eigenvalue λ
In linear algebra, if a is a square real matrix and v is an eigenvector of a corresponding to eigenvalue λ, then v is also an eigenvector of a corresponding to the same eigenvalue λ. The definition of an eigenvector states that it remains unchanged (up to scaling) when multiplied by the matrix, and this property holds regardless of whether the eigenvalue is repeated or not. Therefore, if v satisfies the equation a * v = λ * v, it will still satisfy the same equation when considering the eigenvalue λ.
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(q8) Which of the following is the area of the surface obtained by rotating the curve
, about the y-axis?
The area of the surface obtained by rotating the curve x = y² − 2y + 1, 0 ≤ y ≤ 2 about the y-axis isπ ∫_0^2 [(y-1)^2+1] √[1+4(y-1)^2] dy.Let's work out the solution. We need to apply the formula of surface area by revolving around the y-axis.The surface area is generated by the revolving the curve about y-axis, given as,x = y² − 2y + 1, 0 ≤ y ≤ 2.
Now, we must derive the formula to calculate the area of a surface obtained by rotating a curve around the y-axis. We use the formula given below, which involves integration of the function involved.
Let's see the formula for rotating around the y-axis:Area = 2π ∫_a^b xf(x)dxWe have given x = y² − 2y + 1, 0 ≤ y ≤ 2,To apply the above formula, we need to rearrange the given curve in terms of x,Let x = y² − 2y + 1We can obtain the value of y as, y = 1 ± √(x − 1).The limits of integration of y-axis are 0 and 2.Therefore, the area of the surface obtained by rotating the curve x = y² − 2y + 1, 0 ≤ y ≤ 2 about the y-axis isπ ∫_0^2 [(y-1)^2+1] √[1+4(y-1)^2] dy.
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Let X = R and A = {0, R, {1}, R\{2}}. Then a. A is a o-algebra over R for all x ER. b. A is not a o-algebra over R. c. A is a o-algebra over R for r – 1. d. None of the above.
Let X = R and A = {0, R, {1}, R\{2}}. Then a is option (b) A is not a σ-algebra over R.
To be a σ-algebra over a set X, a collection of subsets A must satisfy three properties:
1. X must be in A.
2. If A is in A, then the complement of A (X\A) must also be in A.
3. If A₁, A₂, A₃, ... are subsets in A, then their union (A₁ ∪ A₂ ∪ A₃ ∪ ...) must also be in A.
Let's examine the given collection of subsets A = {0, R, {1}, R\{2}} over the set X = R.
1. X = R is not in A. (Property 1 is violated.)
2. The complement of {1}, which is R\{1}, is not in A. (Property 2 is violated.)
3. Taking A₁ = {1} and A₂ = R\{2}, their union A₁ ∪ A₂ = {1} ∪ (R\{2}) = {1,2} is not in A. (Property 3 is violated.)
Since A does not satisfy the three properties of a σ-algebra over R, the correct answer is (b) A is not a σ-algebra over R.
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Which expression is equivalent to 5(2+7)?
Answer:
I can help you but first I need the rest of the answers to find out what's it equivalent to.
1
Find the length s of the arc of a circle of radius 9 feet subtended by the central angle
3
radian
s (arc length) =
feet
Answer:
27.0 feet
Step-by-step explanation:
Length of an arc (s) = 2πrθ/360................. Equation 1
Where r = radius of the circle, θ = angle in degree substends by the arc at the center of the circle.
From the question,
Given: r = 9 feet, θ = 3 radian = 3 (57.2950) = 171.89°
Constant: π = 3.14
Substitute these values into equation 1
s = 2(3.14)(9)(171.89)/360
s = 9715.2228/360
s = 26.99 feet
s ≈ 27.0 feet
If the pointer in the figure is spun twice, find the probability that the pointer lands on green (G) both spins.
Answer:
25%
Step-by-step explanation:
The bottom left and top right are each a quarter of the circle and are thus 25% each. The slivers in the middle have to add up to 50% and are all evenly sized. That means that each sliver is 50/4 or 12.5%
Since there are two green slivers, we multiply 12.5% * 2 to get 25%.
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
X=12
Step-by-step explanation:
X²=X×X, so 12×12=144
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]x^{2} =144[/tex]
[tex]x=\sqrt{144}[/tex]
[tex]x=12[/tex]
please help I give brainliest
I don't want to see link if I do you will be reported
Answer:
c(maybe?)
Step-by-step explanation:
dont give me a brainliest.
Which Angle has a corresponding angle of angle 6
Answer:
lines l and m are not parallel so the only angle we can say with certainty that has the same measure as angle 6 is angle 8 because they are vertical angles
Step-by-step explanation:
Which graph represents the function f(x)=−2^x−1?
Answer:
The graph in the bottom right corner
Five more then six times a number is 17.what is the number
Answer:
2
Step-by-step explanation:
You set up and equation:
5+6x = 17
You solve it and get 2.
Step-by-step explanation:
17-5 = 12
What is the volume of the rectangular prism in cubic centimeters?
Here are the ingredients needed to make 16 biscuits.
Biscuits
Ingredients to make 16 biscuits
175 g of butter
75 g of sugar
250 g of flour
Anna has
500 g of butter
300 g of sugar
625 g of flour
Work out the greatest number of biscuits Anna can make.
Answer:
40 biscuits
Step-by-step explanation:
Here are the ingredients needed to make 16 biscuits.
From the above question
Ingredients to make 16 biscuits
175 g of butter
75 g of sugar
250 g of flour
Anna has
500 g of butter
300 g of sugar
625 g of flour
To find the greatest number of biscuits she can make:
For flour
250g of butter = 16 biscuits
625g of butter = x
Cross Multiply
250x = 625 × 16
x = 625 × 16/250
x = 40 biscuits
Maria rides her bike on the same route each day. The table shows the relationship between the days (d) Maria rides her bike and the total miles (m) traveled. Maria's Bike Rides Days (d) Total Miles (m) 4 50 12 150 16 200 24 300 Which equation describes the data in the table? A. m = 12.5d B. m = d + 8.3 C. m = d + 12.5 D. m = 8.3d
Answer:
C
Step-by-step explanation:
Without looking, sam took a colored pencil from his case, which has 1 black, 2 red, 3 blue, 2 yellow, and 1 orange pencil. What's the probability he chose a blue one?
Answer:
3/9 or 1/3
Step-by-step explanation:
help please I have no idea
Answer:
There is nothing here to answer.
Step-by-step explanation:
What the question is asking you to do is
convert
[tex] \frac{20}{200} [/tex]
into a percentage.
First, we will divide the numerator and denominator by 2 to get the denominator to 100 , then from there, we can get the percentage value from the numerator.
[tex] \frac{20 \div 2}{200 \div 2} \\ = \frac{10}{100} [/tex]
From the fraction above, we can see that the 20 is 10% of 200 , from the numerator.
Find two vectors vi and v2 whose sum is (5, -5,5), where vį is parallel to (5,-1, 1) while v2 is perpendicular to (5, -1, 1). V1=__and V2 = __
The required vectors are V1 = (5/√27, -1/√27, 1/√27) and V2 = (1, 2, 3).
Given that the sum of two vectors is (5, -5, 5),
where vį is parallel to (5, -1, 1) while v2 is perpendicular to (5, -1, 1).
Now, let's find vį:
We have, vį is parallel to (5,-1, 1).
Then, a scalar k can be found such that vį = k(5,-1,1)
Using the condition that the magnitude of vį is √23,k can be found as follows:
|vį| = k|(5, -1, 1)|⟹ √(k²(5² + (-1)² + 1²)) = √23⟹ √(27k²) = √23⟹ k = 1/√27
Thus, vį = (5/√27, -1/√27, 1/√27)
Now, let's find v2:We have, v2 is perpendicular to (5,-1, 1).
Thus, the dot product of v2 and (5,-1,1) is zero.
We can write this asv2 .
(5,-1,1) = 0v2 . (5,-1,1) = 5v2₁ - v2₂ + v2₃ = 0
Thus, the vector v2 can be chosen as(1, 2, 3) as the above equation is satisfied by v2 = (1, 2, 3)
Therefore, V1 = (5/√27, -1/√27, 1/√27) and V2 = (1, 2, 3).
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Karen wants to string lights around the edge of her deck. The shape and dimensions of her deck are shown in the diagram
How many feet of lights does she need to get the lights around her deck?
Answer:
She needs 70ft of lights
Step-by-step explanation:
Define: probability sample a) every possible sample of a given size has the same chance to be selected. b) the explanatory variable(s) in an experiment. c) gives each member of the population a known chance to be selected. d) successively smaller groups are selected within the population in stages. e) using extraneous factors to create similar groups. f) people who choose themselves for a sample by responding to a general appeal. g) choosing the individuals easiest to reach. h) directly holding extraneous factors constant. i) population is divided into similar groups and a SRS is chosen from each group.
Answer:
c) gives each member of the population a known chance to be selected
Step-by-step explanation:
A sample is said to be a probability sample when each and every unit of the population would have the known chance or the probability i.e. more than zero when selected in the sample
So according to the given options, it is the sample where each member have the known chance to be selected
Therefore the option c is correct
Which amount is largest?
1 kg
1 dg
100 g
1,000 mg
Answer:
1 kg here you go this is the answer
when drawing a marble from a bag that has 6 pink marbles, 3 blue marbles, and 7 green marbles. What is the probability of green. A) 1/2 B) 7/16 C) 9/16 D) 7/9
Answer:
B
Step-by-step explanation:
The total number of marbles in the bag is 3 + 6 + 7 = 16
The number of green marbles is 7
The probability is 7/16
Factor 21b + 18.
Write your answer as a product with a whole number greater than 1.
plz help
Answer:
3(7b+6)
Step-by-step explanation:
Simply find the greatest common factor between 21b and 18, which is 3. Then that's your simplest factorized expression.
Simplify
3 x 34
leaving your answer in index form.
Answer:
Multiply 34 by 3
102x
two equal sides of a triangle are each 8 m less than six times the third side. if its perimeter is 23 m, what are its side-lengths?
The side lengths of the given triangle are 3 m, 10 m, and 10 m.
Let's assume the length of the third side of the triangle is x.
According to the given information, the two equal sides of the triangle are each 8 m less than six times the third side. Therefore, the lengths of the two equal sides can be expressed as:
6x - 8
6x - 8
The perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given as 23 m:
x + (6x - 8) + (6x - 8) = 23
Simplifying the equation:
x + 6x - 8 + 6x - 8 = 23
13x - 16 = 23
13x = 23 + 16
13x = 39
x = 39 / 13
x = 3
Now that we have the value of x, we can find the lengths of the two equal sides:
Equal side 1 = 6x - 8 = 6 * 3 - 8 = 10 m
Equal side 2 = 6x - 8 = 6 * 3 - 8 = 10 m
Therefore, the side lengths of the triangle are 3 m, 10 m, and 10 m.
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The number of bus riders was recorded on one route. The data have these values: minimum = 18, lower quartile = 22,
median = 26, upper quartile = 29, and maximum = 37.
Which box plot represents the data?
15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31
31 32 33 34 35 36
15 16 17 18
19 20 21
22
20
24
25
26
27
20
20
20
31
32
33 34 35
15 16 17 18 19 20 21
18 19 20 21 22 23 24 25 26 27
25 26 27 28 29 30 31 32 33 34
32 33 34 35 36 37
O
20
15 16 17 18
21 22 23 24 25
26 27
20
29
35
33 34
Answer:
The answer is B
Step-by-step explanation:
I took the test
The box plot that represents the number of bus drivers with the given five-number summary is: option B (see image attached below).
How to Graph A Box Plot?A box plot is graphed to indicate the five-number summary as:
Minimum is represented by the value at the extreme end of the left whiskerLower quartile is at the beginning of the edge of the rectangular boxMedian is at the vertical line dividing the boxUpper quartile is at the end of the edge of the rectangular boxMaximum is represented by the value at the extreme end of the right whisker.Given the five-number summary of the number of bus riders as: minimum = 18, lower quartile = 22, median = 26, upper quartile = 29, and maximum = 37, the box plot that represents the data is: Option B (see image attached below.
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