When does the algebraic multiplicity equal to geometric multiplicity?
The algebraic multiplicity of an eigenvalue equals the geometric multiplicity when the corresponding eigenspace is sufficiently spanned by independent vectors, usually implying that the matrix or linear transformation is diagonalizable.
Explanation:In cases of linear algebra, the algebraic multiplicity of an eigenvalue equals the geometric multiplicity when the respective eigenvector space is completely spanned by independent vectors. Nevertheless, the algebraic multiplicity of an eigenvalue is always greater than or equal to the geometric multiplicity. The situation where algebraic multiplicity is equal to geometric multiplicity generally signifies that the linear transformation or matrix is diagonalizable.
To clarify, the algebraic multiplicity of an eigenvalue is the number of times it appears as a root of the characteristic polynomial, and the geometric multiplicity is the dimension of the corresponding eigenspace. When these two quantities are equal, it often leads to a simpler set of calculations in practical applications of linear algebra.
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Which graph represents the solution to the system of inequalities? y ≥ x – 5 y < –x + 4
The solution to a system of inequalities y ≥ x – 5 and y < –x + 4 is the region where these two inequalities intersect on the graph. This region is below the line y = -x + 4, and also above or on the line y = x - 5.
Explanation:The subject of your concern lies in the field of Mathematics, more specifically, in the topic related to graphical representation of systems of inequalities. To find which graph represents the solution to the system of inequalities y ≥ x – 5 and y < –x + 4, you need to plot both inequalities on the same graph.
For the inequality y ≥ x – 5, plot a line with a slope of 1 and a y-intercept of -5. This line will slope upwards, to reflect that y is greater than or equal to x - 5. For the inequality y < –x + 4, plot a line with slope of -1 and a y-intercept of 4, which will slope downwards as y is lesser than -x + 4.
The region where both these inequalities intersect would be the solution to the system of inequalities. This region would be below the line y = -x + 4, but also above and on the line y = x - 5.
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A graph that represents the solution to the system of inequalities y ≥ x – 5 and y < –x + 4 is shown in the image below.
What are the rules for writing an inequality?In Mathematics, there are several rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:
The line on a graph should be a dashed line when the inequality symbol is (> or <).The inequality symbol should be greater than or equal to (≥) when a solid line is shaded above.The inequality symbol should be less than or equal to (≤) when a solid line is shaded below.In this context, we can logically deduce that the graph of this linear inequality, y ≥ x – 5 would be a solid line and shaded above while the graph of this linear inequality, y < –x + 4 would be a dashed line and shaded below.
In conclusion, a possible solution is (2, 1).
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Missing Information
The question is incomplete. Hence, a general answer was provided.
What is the equation of the line in slope intercept form? if its in points (-2 , 8) (1 , 2) A. -2x-y=-4 B. y=2x-4 C. 2x+y=4 D. y= -2x+4
Final answer:
The equation of the line in slope-intercept form, given the points (-2, 8) and (1, 2), is y = -2x + 4, which is option D.
Explanation:
The question asks for the equation of a line in slope-intercept form given two points on the line (-2, 8) and (1, 2). To find the equation, we first calculate the slope (m) which is the change in y-values divided by the change in x-values. Using the given points,
m = (2 - 8) / (1 - (-2))
= -6 / 3
= -2.
With the slope known, we use one point to solve for the y-intercept (b) in the equation,
y = mx + b.
Let's use the point (1, 2):
2 = (-2)(1) + b, which simplifies to,
2 = -2 + b, so,
b = 4. Therefore, the equation in slope-intercept form is y = -2x + 4, which corresponds to option D.
PLEASE PLEASE HELP!!!!
Given the system of equations, what is the value of the system determinant?
x + y = 8
x - y = 10
A. 0
B. -1
C. -2
Given the system of equations, what is the value of the y-determinant?
3x + y - 10 = 0
4x - y - 4 = 0
A. -28
B. -14
C. 28
Answer:
Given the system of equations, what is the value of the system determinant? x + y = 8
x - y = 10
C. -2
Given the system of equations, what is the value of the y-determinant?
3x + y - 10 = 0
4x - y - 4 = 0
A. -28
Step-by-step explanation:
The determinant of the system is the determinant of the matrix formed with the coefficients of the system, usually, this matrix is called A.
[tex]A=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]
In the 2x2 matrix, the determinant is calculated by obtaining the difference between the diagonally down product and the diagonally up product.
[tex]det(A)=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-1-1=-2[/tex]
The y-determinant is the determinant of the matrix [tex]A_y[/tex], this matrix is formed substituting in the matrix A the coefficients of y with the constant terms.
[tex]A_y=\left[\begin{array}{cc}3&10\\4&4\end{array}\right][/tex]
[tex]det(A_y)=\left|\begin{array}{cc}3&10\\4&4\end{array}\right|=(3)(4)-(4)(10)=12-40=-28[/tex]
How to do this ?? How
Answer: the 3 one is the answer
Write an equation of the parabola with focus (0, −5/3) and directrix y=5/3
I know the formula is y= 1/4p x^2 but i am having trouble with the fractions being implemented.
p=-5/3
If f (x)=5x-7, then what us the solution to f (x)=4
What is the messure of ABC
The high school dance team is learning a new routine to a song that lasts 3 minutes and 41 seconds, or 221 seconds total. Yesterday, they covered the first 45 seconds of the song at practice. They learn an average of 22 seconds of the dance in an hour. Let h represent the time, in hours, it will take the team to learn the entire dance. Which equation represents this situation, and how long will it take?
A. 221 = 22h; 11 hours
B.221 = 22h - 45;12 hours
C.221 = 22h + 45; 8 hours
D. 221 = 45h + 22; 5 hours
Answer:
Option C.
Step-by-step explanation:
High school dance team is learning a new routine to a song that lasts 221 seconds.
Yesterday they covered the first 45 seconds for the song at practice.
They learn an average of 22 seconds of dance per hour.
If they learned the dance for h hours then total time taken for routine will be = (22h + 45)
Therefore, equation that represents the this situation will be
22h + 45 = 221
22h = 221 - 45
22h = 176
h = [tex]\frac{176}{22}=8[/tex]
Total hours taken will be 8 hours.
Therefore, option C will be the answer.
can you form an angle bisector hen the angle is a straight line?
order :5/6,1/8,5/16,7/12 on the number line
Numberline: 0 ------------------------1
How to solve exterior angle for right triangle?
In 2012 your car was worth 12500 in 2014 your car is was worth 8500 linear function to determine the cars value
Is an equation used to compute probabilities of continuous random variables
Lydia inherited a sum of money. She split it into five equal parts. She invested three parts of the money in a high-interest bank account which added 10% to the value. She placed the rest of her inheritance plus $500 in the stock market but lost 20% on that money. If the two accounts end up with exactly the same amount of money in them, how much did she inherit?
Adam and Barb had a book sale over the weekend. Adam sold 4 hardcover books and ten paperbacks. Barb sold 5 hardcover books and 7 paperbacks for the same prices each. Adam sold $62 worth of books while Barb sold $61 worth. How much did they charge for hardcovers and how much for paperbacks?
What is your understanding of the problem
. What is being asked and what will answer the question? Do not just copy the problem! Mathematically what kind of problem is this?
What skill or concept did we learn in this unit which, when applied to this problem, will allow you to solve the problem?
Show the equations you’ll use to set up the problem.
Be sure to label or explain what your variables mean.
Show the math work to arrive at the answer.
Write your final answer. Be sure to make it clear which is hardcover and which is paperback.
A malapropism occurs when two people use the same word to mean two different things
Final answer:
A malapropism occurs when two people use the same word to mean two different things. It is a form of linguistic humor that often involves the inadvertent substitution of one word for another that sounds similar but has a completely different meaning.
Explanation:
A malapropism occurs when two people use the same word to mean two different things. It is a form of linguistic humor that often involves the inadvertent substitution of one word for another that sounds similar but has a completely different meaning. An example of a malapropism is when someone says, 'I have a photographic memory. I can remember everything - even the things that never happened.'
Ebony earns $2,000 per month. If she spends $450 on rent each month, what percent of her income does she spend on ren
The sum of two numbers is 46 and the difference is 12 what are the numbers?
Simplify the expression. (–9m + 12) –6m + 12 –6m + 8 –6m + 24 –18m + 8 Description
Answer:
-45m + 64
Step-by-step explanation:
To solve this, we are going to eliminate the parenthesis first:
(–9m + 12) –6m + 12 –6m + 8 –6m + 24 –18m + 8
= -9m + 12 - 6m + 12 –6m + 8 –6m + 24 –18m + 8
Now we're going to sum up all the terms that have an "m" and all the independent terms
=(-9m -6m - 6m - 6m - 18 m) + (12+12+8+24+8)
= - 45m + 64.
Thus, the expression is -45m + 64.
HELP!!! I got the first part done but I feel as though I did it wrong because I can't seem to get part 2 or 3 done.
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
f(x) = ax^2 + bx + c a = 1 b = 4 c = 6 (x – a) a = -2
f(x) = x^2 + 4x + 6 (x – 2)
Part 1. Show all work using long division to divide your polynomial by the binomial.
X + 4
x-2√(x^2+4x+6)
-x^2+2x
6x + 6
- 6x + 12 18 is the remainder of x + 4
18 x + 4 + 18/(x-2)
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function
Answer:
It's all below...
Step-by-step explanation:
Part 1.
quadratic poynomial function: f(x)=x2−5x+6
linear binomial: x−2
x−3x−2x2−5x+6x2−2x−−−−−−−−−−3x+6−3x+6−−−−−−−−0
Part 2.
f(2)=22−5(2)+6=4−10+6=−6+6=0
Part 3.
The remainder theorem says that if f(x) is divided by x-a, then f(a) will be the remainder. When we divided f(x) by x - 2 , we got a remainder of 0, which by the remainder theorem implies f(2) = 0. That means x-2 is a factor of f(x).
What is the best metric unit to measure the distance from ohio to texas?
PLEASE HELP ME OUT ASAP
If r^n=a then which of the following are true statements??
A. a^r=n
B. n^1/r=a
C.a^1/n=r
D.n sqrt a=r
PLEASE HELP ASAP!!!! :)
Identify the natural number that is closest to √142.
A.) 11
B.) 12
C.) 142
D.) 13
What is the tangent of angle a?
a. 6/8
b. 8/10
c. 8/6
d. 6/10
Use the discriminant to determine the number and type of solutions for the given equation x^2+2x+6=0
What is the range for the function ƒ(x) = 7?
Graph y−5=−2/3(x+9) using the point and slope given in the equation.
YOU NEED A GRAPH
see attached sketch with the coordinates the line passes
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Find the least number which must be added to 1825 to get a perfect square find the square root of the perfect squre so obtained
PLEASE ANSWER ASAP!!!
Identify the natural number that is closest to√98.
A.) 10
B.) 98
C.) 11
D.) 9