No, A is not defective.
What is the rank nullity theorem?The rank–nullity theorem is a theorem in linear algebra, which asserts that the dimension of the domain of a linear map is the sum of its rank (the dimension of its image) and its nullity (the dimension of its kernel).
Given here A be a 4 x 4 matrix and let λ be an eigenvalue of multiplicity 3 and rank 1, then by rank nullity theorem we have
Rank(A-λI) + Nullity((A-λI) =4
⇒dimN(N-λI) = Nullity(A-λI)
⇒dimN(N-λI) = 4 - Rank(A-λI)
⇒dimN(N-λI) = 4-1
⇒dimN(N-λI) = 3
Therefore 3 linearly independent eigenvectors belong to eigenvalue λ. Since λ is an eigenvalue of multiplicity 3, this ensures that there is a different eigenvalue different from λ. Along with 3 linearly independent eigenvectors in the eigenspace of λ, this gives us 4 linearly independent eigenvectors in the matrix A. Now we An n × n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. Thus A is nondefective
Hence, matrix A is not defective.
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What is the value of the smaller zero of the function f(x) = 2x2 - 8x - 24?
hi can anyone help me with this please
Answer:35in.
Step-by-step explanation:
I reccomend splitting it into sections when given problems like this.
The smaller two rectangles would be 5in * 2in which is 10in then just add them together.
For the bigger one, you'd do 5-2 in order to get the missing inches which will be 3+2 once added 5in*3in is 15in.
Finally, add 15+10+10 (15=The middle rectangle and 10=the sides)
Answer:
Break it up into pieces. The answer is 35in^2
Step-by-step explanation:
I took the first rectangle you see which is 5in by 2. Multiply that and you get 10
I then took the second one and is the 5 in by 3in. Multiply those and you get 15
The last one is the exact same as the first one
Add the areas all together and you get the area of the whole shape
Hope that helps
Find the area of the figure
Answer:
145.1327
Step-by-step explanation:
Divide the given figure up into two smaller figures. Calculate the area of each of the smaller figures and then add up the areas. One can divide this figure into a rectangle with sides (8 and 15), and a semi-circle with a diameter of (8m).
Calculate the area of the rectangle, the formula to calculate the area of a rectangle is ([tex]base*height[/tex])
8 * 15 = 120
Calculate the area of the semi-circle. The formulas for the area of a semi-circle is the formula for the area of a circle divided by (2), ([tex]A=\frac{(pi)r^2}{2}[/tex]). Where (A) represents the are, (pi) represents the number (3.1415...), and (r) represents the radius of the circle. The radius is always half of the diameter of a cricle. Substitute in the given values, and solve
[tex]\frac{(pi)(\frac{8}{2})^2}{2}[/tex]
[tex]=\frac{(pi)(4)^2}{2}[/tex]
[tex]=\frac{(pi)16}{2}[/tex]
[tex]=8(pi)[/tex]
~25.1327
Now add up the two values,
120 + 25.1327
= 145.1327
the larger of two numbers is twice the smaller. if the larger is x what is the smalller. I NEED HELP PLSSS!!
Answer:
Easy. The smaller is x/2.
Step-by-step explanation:
2 times is larger, so larger divided by 2 is the smaller.
expand expression (3x-7)(2x+7), without using long multiplication find 53×47
Answer:
6x² + 7x - 49
53×47 = 2491
Step-by-step explanation:
(3x-7)(2x+7)
6x² + 21x - 14x - 49
combine like terms:
6x² + 7x - 49
What is the area of this parallelogram?
104 m²
88 m²
56 m²
32 m²
Answer: To find area of a rectangle, multiply its base (length) by its height (width). Plug in the base, 7 meters, and the height, 8 meters. So the area of Rectangle DFBE is 56 square meters.
88m
HOPE THIS HELPS
A simple random sample of size 51 has sample mean of 70.72. The population distribution is approximately normal, with population standard deviation of 16.25. Determine the correct method of finding a 95% confidence interval for the unknown population mean and compute it. z-method: (66.26, 75.18) Cannot compute: the population size is too small. t-method: (66.15, 75.29) z-method: (66.15, 75.29)
Answer:
z-method: (66.26, 75.18)
Step-by-step explanation:
We have the standard deviation for the population, which means that we use the z-distribution to solve this question.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{16.25}{\sqrt{51}} = 4.46[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 70.72 - 4.46 = 66.26
The upper end of the interval is the sample mean added to M. So it is 70.72 + 4.46 = 75.18
The correct answer is z-method: (66.26, 75.18)
the length and the breadth of a rectangular Garden are 0.8 km and 0.6 km respectively find the length of a wire required to put a fivefold fans around the garden
Answer:
Length of wire required for 5 fold of garden = 14 km
Step-by-step explanation:
Given:
Length of rectangle garden = 0.8 km
Width of rectangle garden = 0.6 km
Find:
Length of wire required for 5 fold of garden
Computation:
Perimeter of rectangle = 2[l + b]
Perimeter of garden = 2[0.8 + 0.6]
Perimeter of garden = 2[1.4]
Perimeter of garden = 2.8 km
Length of wire required for 5 fold of garden = 5 x Perimeter of garden
Length of wire required for 5 fold of garden = 5 x 2.8
Length of wire required for 5 fold of garden = 14 km
Hi, I need the are to this question, I just need to show my work btw
Write the equation for the line that passes through the points (3, 18) and (-3,0)
a set of speakers that regularly cost $160 are on clearance for 35% off. Find the sales price of the speakers
Answer:
I'm pretty sure this is the answer....
The speakers are $56.
Sorry if i'm wrong. :')
Step-by-step explanation:
Answer:
You want to buy something that costs $160, and it's on sale for 35% off. What is the item's sale price?
First, convert the 35% to a real mathematical number. For percents, this is always done by dividing the 35% by 100%, or 35% / 100% = 0.350.
Second, find out what 35% of $160 is. This is the amount of the sale discount. This is always found by mulitplying 0.350 by the item's cost $160, like this:
0.350 x $160 = $56.00.
So for this sale, you'll save $56.00 on this item.
This means, the cost of the item to you is
$160 - $56.00 = $104.00.
Alternatively, you can think about it this way. The item is 35% off. This means you'll pay 65.000% of the total cost (100% - 35% = 65.000%).
Now what's 65.000% of the total cost?
0.650 x $160 = $104.00.
Just like the result above, the sale price on the item is $104.00
Answer it right and i'll try to give you brainliest.
Answer:
384 cm²
Step-by-step explanation:
Since it is a square pyramid, the total surface area of the pyramid is the area of its square base plus the area of its 4 triangular faces.
[tex]\boxed{area \: of \: triangle = \frac{1}{2} \times base \times height }[/tex]
Area of a triangular face
= ½ ×12 ×10
= 60 cm²
[tex]\boxed{area \: of \: square = side \times side}[/tex]
Base area of pyramid
= 12 ×12
= 144 cm²
∴ Surface area of pyramid
= 4(60) +144
= 240 +144
= 384 cm²
Make a box-and-whisker plot for the set of data.
21, 27, 27, 25, 21, 13, 18, 25
jasonran 4 miles in 30 minutes which of the following is an equivalent rate of running
Answer:
10 miles in 75 minutes
Step-by-step explanation:
Help please will mark brainliest!!!
Answer:
176.71
Step-by-step explanation:
you can just search up "area of circle calculator and plug in the radius
Alejandra took a taxi home from the airport. The taxi fare was $2 per mile,
and she gave the driver a tip of $5. She paid a total of $49. How far is it from
the airport to Alejandra's home?
Answer:
22 miles
.......ur welcome.......
49-5=44
44÷2=22
Answer:
The answer is 22miles from the airport to Alejandra's home.
Step-by-step explanation:
2 X 22 = $44
PLUS $5 dollar tip so that would be:
$44 + $5 = $49
Find the area of the polygon to the nearest square inch.
Answer: 70
Step-by-step explanation:
Sammy draws 3 identical rectangles on his paper. If each rectangle has a base of 15 cm and a height of 12 cm, what is the total area of all 3 rectangles added together?
Answer:
540
Step-by-step explanation:
If you do 15x12 which is the formula for area for a rectangle, you get 180. That's only the area of one rectangle but if you multiply it by 3 you get 540 for the areas added together.
Answer:
540 cm
Step-by-step explanation:
you multiply 15 x12 If you are getting an area 15 x12=180 then you multiply 180 by 3 180x3=540 I think
Evaluate x2 + 6, when x=8
Help.
JOE CAN READ 27 PAGES IN 3 HOURS. HOW MANY CAN HE READ IN 9 HOURS?
perimeter 254 meters and dimension measures 6 meters
Answer:
didn't even ask a question
Step-by-step explanation:
impossible to answer without a question
Maria and Veronica go to a restaurant Maria orders 4 taco’s and a drink, and pays $7. Veronica orders 3 taco’s and two drinks, and pays $7.75. Write a system of equations and solve to find the cost of each taco and drink.
Answer:
y=7+4 and y=7+3
Step-by-step explanation:
which of these describes abc?
Answer:
A
Step-by-step explanation:
I remember it by:
acute: a cute little angle that is smaller than 90 degrees
Josephine owns a dress shop and purchases a dress for $20. She decides to mark up the dress 35% in order to sell it to her customers. What is the amount of profit Josephine will make when she sells a dress to a customer? o Josephine will make a profit of $35 O Josephine will make a profit of $27 O Josephine will make a profit of $10 O Josephine will make a profit of $7
Answer:
Josephine will have $15 profit
PLEASE HELP FAST ILL MARK AS BRAINLIEST!!!!! :((
Solve this and put it an inequality.
|x - 7|=x-7
Answer:
x>=7
Step-by-step explanation:
Since the equation on the right is equal to the equation on the left that means that x has to be greater or equal to 7 to make the statement true.
Which is bigger 3/12 or -4/5
Step-by-step explanation:
3/12 = 0.25
-4/5 = - 0.8
so since the 2nd one is negative.
so 3/12 is the bigger
(-4x + 5) - (6x + 7) = 0
What is the solution to the equation?
O x = 6
O x= 1
O x = -0.2
O = -1.2
A point is chosen at random on AK.
What is the probability that the point
will be on FI? Don't forget to reduce.
A B с E F G H I J KI
HHHHHHHHHHHHHH
-10 -8 -6 -4 -2 0 2 4 6 8 10
Answer: 3/10
Step-by-step explanation: 6/20 reduced = 3/10 for acellus
Probability -
Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail).Given,
A B с E F G H I J KI
HHHHHHHHHHHHHH
-10 -8 -6 -4 -2 0 2 4 6 8 10
So,
The probability that the point will be on FI
A B KI C D E E G H J
HHHHHHHHH
-6 -4 -2 0 2 4 6 8 -10° -8 10
Enter Done q W er t y u i O p a a s d f f gh j k Z X C V b n m X 123 space return .
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Find the volume of the cylinder. Round your answer to the nearest tenth.
3ft.
10 ft.
Enter only the numerical value with the units of measure.