Characteristic polynomial of the matrix [tex]p(x) = (x+1)(x-2)^2[/tex]
For the matrix [8 -4 0 -4], the characteristic polynomial is found by taking the determinant of the matrix [8-x -4 0 -4; 0 8-x -4 0; 0 0 8-x -4; 0 0 0 8-x] and simplifying it. This results in p(x) = [tex](x-8)^4[/tex].
For the matrix [3 0 4 -3 -4 -1 0 -1 0], the characteristic polynomial is found by taking the determinant of the matrix [3-x 0 4; -3 -4-x -1; 0 -1 -x 0;] and simplifying it. This results in [tex]p(x) = (x+1)(x-2)^2[/tex].
The determinant of the matrix (A - lam*I), where I is the identity matrix of the same size as A, is found by computing the characteristic polynomial of a square matrix A, represented by P(lam), which is a polynomial function of a scalar variable lambda. We refer to the eigenvalues of the matrix A as the roots of the characteristic polynomial. Important details about the matrix, including its diagonalizability, rank, trace, and determinant, are revealed by the characteristic polynomial. It frequently appears in applications like systems of linear equations, differential equations, and linear transformations.
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Micah is saving money for his first car his parents gave him 250 for his birthday and each week he plans on putting $40 into his savings account
Answer:
whats the question though?
Use the equation below to find the y, M=11, x=2 and B=5
Answer:
The length and breadth of a rectangular
field are equal to 600 m and 400 m
respectively. Find the cost of the grass to be
planted in it at the rate of ₹ 2.50 per m2
14% of math students got an A on the test. 29% got a B. What percentage of students got a C, D, or an F?
Answer:
57% of students
Step-by-step explanation:
14 + 29 = 43%
100% - 43% = 57%
Can you help me with this pls?
Find the product (x + 4)
Answer:
4x
Step-by-step explanation:
It would be 4x because you have no value given of the variable "X"
therefore, your answer would just be adding the x to the 4 making it 4x
hope this helped!
it’s sad when I help people because they can’t do the same thing for me pls just for once answer this pls :(((((((
Answer:
D
Step-by-step explanation:
It compares two values.
Hope this helps!
Answer:
D because it have asked the question
Which functions readily show the y-intercept of their graphs?
Answer:
to find your y intercept use y= mx + c
help please!!!!!!!!! Which image is a reflection of the black polygon in quadrant I?
On a coordinate plane, the black polygon is reflected across the y-axis to form the red polygon.
the black polygon in quadrant I
the red polygon in quadrant II
the blue polygon in quadrant III
the green polygon in quadrant IV
Answer:
The red polygon
Step-by-step explanation:
Think of the quadrants:
The "top right" one is quadrant I
The "top left" one is quadrant II
The "bottom left" one is quadrant III
The "bottom right" one is quadrant IV
When it says "reflected across y-axis", think of the y-axis as a "mirror"
Since the black polygon is in quadrant I, think of it looking into the mirror, or y axis. It is reflecting into quadrant II.
The red polygon is in quadrant II.
Sorry! I know this is a really weird explanation, but hope it helps!
Answer: The answer is the red polygon in quadrant ll (B)!
- just like the person above
Step-by-step explanation:
Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?
Answer:
£7.3
Step-by-step explanation:
2 x £2=£4
3 x £3 = £6
3 x 90 = 270 = £2.7
£4+£6+£2.7= £12.7
20-12.7=7.3
7 pounds and 3
Answer: 4.3
Step-by-step explanation:
2(2)+3(3)+3(.9)=
4+9+2.7=15.7
20-15.7= 4.3
I'm assuming that 100 p is 1 £, if that's not the case this would be wrong
Please help, and show steps :)
6(5 - q) ?
This is distributive property of multiplication.
Answer:
30-6q
Step-by-step explanation:
6*5-6*q
30-6q
Four triangles with bases of 12 centimeters and heights of 8 centimeters were used to form a parallelogram. Calculate the area of the parallelogram.
Answer:
192
Step-by-step explanation:
12 x 8 x 4 x1/2 = 192
192
In Will’s garden, 71 out of 200 plants have developed seeds. Which is closest to the percent of his plants that have developed seeds?
A. 20%
B. 35%
C. 70%
D.25%
Evaluate 10m + n²/4 when m=5 and n=4
Answer:
16.5
Step-by-step explanation:
Break down the equation:
10*5=50
4 with an exponent of 2= 16
Then you have: 50+16 / 4
You can simplify it to 66/4
Finally, divide 66 by 4 which equals 16.5
Hope this helps!
Need help ASAP
48 ÷ 2 (9 + 3) = ?
Answer:
I think the answer is 288
Step-by-step explanation:
I think this because 48/2=24 and 9+3=12 (parentheses means multiply) 24x12=288
A 20 feet tree casts a shadow that is 32 feet long. What is the distance from the top of the tree to the tip of the shadow?
Answer:
37.7359
Step-by-step explanation:
first you visualize the shape created
if you visualize it... it will look like a right angled triangle
and we are looking for the longest side
remember the pythagoras theorem c^2= a^2 + b^2
in this case we are looking for c
a^2= 20^2
b^2= 32^2
400+ 1024= 1424
therefore c^2= 1424
then you square root 1424
to get 37.7359
note- the answer is solely based on the information given
The Rugby coach purchased team jerseys for $800 and paid 14% tax. What was her final bill? Question 26 options:
Answer:
The final bill was $912
Step-by-step explanation:
Since there is 14% tax in order to get the final cost we would need to multiply the cost of the jerseys by 1.14, and so we get...
800 x 1.14 = $912
Write as a fraction and fractional model model: there is one container of fruit juice and 2 people want juice
Question seems incomplete but we would make assumptions in order to answer and explain
Answer and explanation:
If we wish to model this situation in the form of a fraction: there is one container containing 30 cans of fruit juice and 2 people want fruit juice, we would be finding how many fruit juice each person would get from the container.
Given one container= 30 cans of fruit juice
Number of persons that require fruit juice = 2
Therefore fraction of fruit juice in relation to required fruit juice= 30/2
52.7 × 12= ?
help again huhuhu
Answer:
632.4
Step-by-step explanation:
Please help me...????
Answer:
el área es el número el 19
Help me somebody please
what is the value of x in 75x -89 ÷ 7791 +7829 ×8391 =314682
At which root does the graph of f(x) = (x – 5)2(x + 2)2 touch the x-axis?
-5
0-2
2
05
Answer:
Option B & D
Step-by-step explanation:
Function is;
f(x) = (x - 5)³(x + 2)²
We want to find the point in thich the graph of this function touches the x-axis.
Usually, the point at which the graph touches the x-axis means that y is 0 at that point.
Thus;
(x - 5)³(x + 2)² = 0
This means that;
x - 5 = 0 and x + 2 = 0
Thus,x = -5 and x = -2
Write 80.75 correct to the nearest whole number.
Answer:
81
Step-by-step explanation:
Dan is stocking up on AA and AAA batteries. He bought 10 packages of batteries for a total of 72 batteries. The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write, but do not solve, a system of equations that can be used to find how many packages of each type of battery Dan bought.
Answer:
x + y = 10
6x + 8y = 72
Step-by-step explanation:
Number of packages = 10
Total batteries = 72
For AA:
batteries per package = 6
Let number of packages = x
For AAA:
batteries per package = 8
Let number of packages = y
Number of AA packages + number of AAA packages = 10
Sum of AA + sum of AAA equals 72 batteries
x + y = 10
6x + 8y = 72
Answer:Answer:
x + y = 10
6x + 8y = 72
Step-by-step explanation:
Number of packages = 10
Total batteries = 72
For AA:
batteries per package = 6
Let number of packages = x
For AAA:
batteries per package = 8
Let number of packages = y
Number of AA packages + number of AAA packages = 10
Sum of AA + sum of AAA equals 72 batteries
x + y = 10
6x + 8y = 72
Step-by-step explanation:
The coordinate bridge shows the cost of different numbers of bookmarks how many sense do for bookmarks cost.
Answer:
54 cents
Step-by-step explanation:
The cost of bookmarks relating to the number of bookmarks is given by the graph shown. Therefore:
From the graph, we can determine the relationship between the cost of bookmarks and the number of bookmarks by using two points. The equation of a line passing through points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\[/tex]
From the graph, y represents the cost of bookmarks in cents and x represent the number of bookmarks. we can see that it passes through the point (2, 30) and (7, 90). Hence:
[tex]y-30=\frac{90-30}{7-2}(x-2)\\\\y-30=12(x-2) \\\\y-30=12x-24\\\\y=12x+6[/tex]
The cost of 4 bookmarks (x = 4):
y = 12(4) + 6
y = 54 cents
HELP PLEASE! ( number 7 btw ) please help this if half of my grade
Answer:
A,B,&E are definitely 7 or more
What does linear mean and what does a linear graph look like?
Kim got to the grocery store at 11:19 in the morning. She spent 24 minutes in the store. Find the points on the number line that show the number of minutes after 11:00 when she got to and left the store.
Answer:
43 minutes
Step-by-step explanation:
Arrival time at grocery store = 11:19 a.m
Time spent in store = 24 minutes
Number of minutes after 11:00 a.m when she arrived and left the store :
Time she left the store :
11:19 a.m + 24 minutes = 11:43 a.m
Minutes after 11:00 when she left :
11:43 - 11:00
= 43 minutes
which statement is true
Answer:
The correct answer would be C Reason being the same angle stays the same after the rotation