To find 2 x 2 matrices A that satisfy A² = I, we can consider matrices that have diagonal entries of 1 and off-diagonal entries of 0 or ±1. The matrices that satisfy this condition are A = [[1, 0], [0, 1]].
A = [[-1, 0], [0, -1]]. These matrices, when squared, give the identity matrix I.
For a 2 x 2 matrix A, the condition A² = I implies that the matrix A, when multiplied by itself, gives the identity matrix. We can consider matrices with diagonal entries of 1 and off-diagonal entries of 0 or ±1. The matrices that satisfy this condition are A = [[1, 0], [0, 1]] and A = [[-1, 0], [0, -1]].
When we square these matrices, we get A² = [[1, 0], [0, 1]] for both cases, which is equal to the identity matrix I. Therefore, these matrices satisfy the condition A² = I.
In general, for an n x n matrix A, there can be other matrices that satisfy A² = I, but for the specific case of 2 x 2 matrices, the matrices mentioned above are the only ones that satisfy the condition.
The trace of a matrix A, denoted as tr(A), is defined as the sum of the diagonal entries of the matrix. To prove that tr(A + B) = tr(A) + tr(B) for matrices A and B of the same size, we can simply expand the sum of the diagonal entries for both matrices A and B and observe that the summation can be carried out separately for each matrix. Thus, the sum of the diagonal entries for A + B will be equal to the sum of the diagonal entries for A plus the sum of the diagonal entries for B. This establishes the desired result, tr(A + B) = tr(A) + tr(B).
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A forest covers 72,000 acres. A survey finds that 0.3% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
21,600 acres of old-growth trees
Step-by-step explanation:
Mtiply 72,000 by 0.3%
0.3 * 72,000 = 21.6k (21,600)
The price of an article with 13% VAT is Rs. 2,034. What is
the price of same article without VAT? Find it.
Step-by-step explanation:
Hey there!
Given;
Vat%= 13%
Price after 13% vat = Rs. 2034
Price without vat = x
Then,
Price with vat= price with out vat + vat% of price with vat.
[tex]2034 = x + \frac{13}{100} \timesx [/tex]
[tex]2034 = \frac{100x + 13x}{100} [/tex]
[tex]2034 \times 100 = 113x[/tex]
[tex]x = \frac{2034 \times 100}{113} [/tex]
x = Rs.1800.
Therefore, the price without vat is Rs.1800.
Hope it helps...
Ali currently has $25. He is going to start saving $5 every week.
Which equation represents this situation?
Answer:
y=5x+25
Step-by-step explanation:
5 is the slope and 25 is the y-intercept
Answer:
5x+25 and the second part is YES
Step-by-step explanation:
10 points
Which equation best represents the relationship between the x and y values?
Х
Y
-2
7
2
-5
4
-11
6.
-17
10
-29
A y = x + 9
B y = x2 + 3
Cy=-3x + 1
Dy = x-7
Answer: C) y = -3x + 1
Step-by-step explanation:
x y
-2 7
2 -5
4 -11
6 -17
10 -29
Choose any two coordinates to find the slope: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
m = -6/2
= -3
Choose any point and plug it into the Point-Slope formula: [tex]y-y_1=m(x-x_1)[/tex]
y - 7 = -3(x + 2)
y - 7 = -3x - 6
y = -3x + 1
Is this correct? If not, tell me what mistakes I made. Thank you
Answer:
LOOKS GREAT!!!
Step-by-step explanation:
HOPE YOU DO WELL!!!
||x-4|-2|<3
Solve for X
Answer:
x<11
Step-by-step explanation:
x−4(|−2|)<3
Simplifies to:
x−8<3
Let's solve your inequality step-by-step.
x−8<3
Step 1: Add 8 to both sides.
x−8+8<3+8
x<11
x2 - 6x – 16
factoring
Answer:
(x-8)(x+2)
Step-by-step explanation:
add to -6 and multiply to -16
-8,2
decomposition of ni3 produces nitrogen gas and iodine. how many grams of the reactant would be required to react completely to give 1.18 g of the iodine?
The decomposition of Ni3 produces nitrogen gas and iodine. How many grams of the reactant would be required to react completely to give 1.18 g of iodine?To begin with, write the balanced equation for the decomposition of Ni3:2Ni3(s) → 3I2(s) + N2(g)
From the balanced equation above, the stoichiometric ratio between Ni3 and I2 is 2:3 that is, for every 2 moles of Ni3 decomposed, 3 moles of I2 is produced.To find the mass of Ni3 that would produce 1.18 g of I2, we need to find the number of moles of I2 produced first.The molar mass of I2 = 253.8 g/molNumber of moles of I2 produced = Mass / Molar mass = 1.18 / 253.8 = 0.004645 molFrom the stoichiometry, 2 moles of Ni3 produce 3 moles of I2, which can be written as:2 mol Ni3 → 3 mol I2
The number of moles of Ni3 that would produce 0.004645 mol of I2 can be obtained using the ratio:2 mol Ni3 / 3 mol I2 = 0.6666667 mol Ni3The mass of Ni3 required to produce 1.18 g of I2 can be obtained by multiplying the number of moles of Ni3 obtained above by the molar mass of Ni3:Mass = moles x molar mass = 0.6666667 x 100.7= 67.11 gTherefore, 67.11 g of Ni3 would be required to react completely to give 1.18 g of iodine.
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I need help detrmine the slope
Answer:
slope = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (8, 6)
m = [tex]\frac{6+4}{8-0}[/tex] = [tex]\frac{10}{8}[/tex] = [tex]\frac{5}{4}[/tex]
25 times the sum of X and Y? and 8 more than the quotient of q and t?
Answer:
this hard
Step-by-step explanation:
Rational number arithmatic
Answer:
A and D are the ones that are right
Answer:
a and d
Step-by-step explanation:
A bag has 2 baseballs (B), 5 tennis balls (T), and 3 whiffle balls (W) What is the probability of pulling out a baseball? Enter your answers in this order: reduced fraction, decimal, and then percent.
Answer:
1/5
.2
20%
this is just filling so I can post this
The probability of pulling out a baseball is 1/5 or 0.2 or 20%.
What is probability?Probability is simply how likely something is to happen.
[tex]P(pulling\ out\ a\ baseball) = \frac{numbers\ of\ baseball}{total\ numbers\ of\ balls }[/tex]
P(pulling out a baseball) = 2/10 = 1/5 = 0.2 = 20%.
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Let f(x)= ax^2+bx+c and g(x)= ax^2-bx+c. If f(1) = g(1)+2 and f(2)=2, find g(2).
Answer:
first lets calculate f(1)=g(1)+2
a+b+c=a-b+c+2 so b=1
next lets calculate f(2)=2 remembering that we found b=1
4a+2*1+c=2 so c=-4a
Now lets find g(2)
g(2)=4a-2b+c= -c-2+c=-2 this is the final response
Sam was asked to place the numbers shown below in order from greatest to least.
1,-0.5, 4, 350%, -1, 4.7, -66, 1.22
After ordering the numbers from greatest to least, what number would Sam have in the fifth position?
A. 122
B. O 350%
C.O}
D.O
Answer:7 2 w
Step-by-step explanation:
Jsjw22
please HELPPPP GONNA GIVE BRAINLIEST!!!!
Answer:
The third answer: -7/8
Step-by-step explanation:
Having the numerator negative makes the entire fraction negative. If both the numerator and the denominator are negative it means that the fraction is positive. So -7/8 is equal to - 7/8.
Hope This Helps :)
Solve this problem, and identify the percent, amount, and base. What percent of 50 is 20 ? Percent =40, Amount =20, Base =50
Percent =40, Amount =50, Base =20
Percent =50, Amount =10, Base =20
Percent =20, Amount =10, Base =50
The percentage of 50 that is 20 is 40 percent. The correct option therefore is the first option;
Percent = 40, Amount = 20, Base = 50What is the formula for finding a percentage?The percentage of an amount within a base can be found using the formula;
Percent = (Amount/Base) × 100
Therefore, the percentage an amount represents in a base can therefore be found using the above formula.
The percentage required is the percentage in 50 represented by 20
Therefore the percentage is; Percent = (20/50) × 100 = 40%
The correct option is therefore;
Percent = 40, Amount = 20, Base = 40
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Help please answer question
Answer:
5
Step-by-step explanation:
The greatest common factor of 60w5y3 and 78 wy2 is
6 wy2
6 w5y3
13 w5y3
2 wy2
Answer:
is that a question
Step-by-step explanation:
What is the standard form of this complex number? (24 - 10i) - (43 + 18i)
Answer:
-19-28i
Step-by-step explanation:
Answer:
-19-28i
Step-by-step explanation:
.There is an island in which certain inhabitants called "knights" always tell the truth, and others called "knaves" always lie. We assume that all of the inhabitants are either knights or knaves. Match the statements on the left with the types on the right. (Based on a series of puzzles by Raymond Smullyan)
Answer:
Step-by-step explanation:
READ A BOOK
find the value of x or y so that the line through the points has the given slope. (7, -3) and (9, y) and Slope is 9/2
Answer:
almost answer
Step-by-step explanation:
A project has an initial cost of $40,400, expected net cash inflows of $14,000 per year for 9 years, and a cost of capital of 12%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round your intermediate calculations. Round your answer to the nearest cent.
Answer:
$59,750
Step-by-step explanation:
According to the given situation, the calculation of net present value is shown below:-
Net present value = Net cash inflows × PVIFA factor(9,12%) - Initial cost
= $14,000 × 7.1607 - $40,400
= $100,250 - $40,500
= $59,750
Therefore as per the situation for computing the net present value we simply applied the above formula.
A business orders 330 flowers for their employees on Valentine's Day. Roses cost
$4.50 each, carnations cost $3.00 each, and lilies cost $2.50 each. There are 20
more lilies than roses. The total of the order came to $1,080.00. How many of each
type of flower were ordered? Write a system of equations that represents the
scenario.
Answer:
Roses = x = 100
Carnations = y = 110
Lilies = z = 120
Step-by-step explanation:
Roses = $4.50
Carnations = $3.00
lilies = $2.50
Total flowers ordered = 330
Total cost = $1,080
Let
Roses = x
Carnations = y
Lilies = z
x + y + z = 330
4.50x + 3y + 2.50z = 1080
There are 20
more lilies than roses
z = x + 20
Substitute z = x + 20 into the equations
x + y + (x + 20) = 330
4.50x + 3y + 2.50(x + 20) = 1080
x + y + x + 20 = 330
4.50x + 3y + 2.50x + 50 = 1080
2x + y = 330 - 20
7x + 3y = 1080 - 50
2x + y = 310 (1)
7x + 3y = 1030 (2)
Multiply (1) by 3
6x + 3y = 930 (3)
7x + 3y = 1030 (2)
Subtract (3) from (2)
7x - 6x = 1030 - 930
x = 100
Substitute x = 100 into (1)
2x + y = 310
2(100)+ y = 310
200 + y = 310
y = 310 - 200
= 110
y = 110
Substitute the value of x and y into
x + y + z = 330
100 + 110 + z = 330
210 + z = 330
z = 330 - 210
= 120
z = 120
Roses = x = 100
Carnations = y = 110
Lilies = z = 120
The table below gives the lengths of the three sides of four triangles. Which triangle is NOT a right triangle?
Triangle A
Triangle B
Triangle C
Triangle D
Answer:
D
Step-by-step explanation:
(a^2)+(b^2)=c^2
Find the line that is perpendicular to line n that passes through point (2, –3).
If the slope of the perpendicular line is -2/5, what is the y-intercept of the perpendicular line?
b = negative StartFraction 19 Over 5 EndFraction
b = negative StartFraction 11 Over 5 EndFraction
b = four-fifths
b = 2
Answer:
its b
Step-by-step explanation:
Answer:it’s b
Step-by-step explanation:
how are Mass and distance related to gravity
Answer:
here.
Step-by-step explanation:
The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them. This means that the force of gravity increases with mass, but decreases with increasing distance between objects.
I hope this helps! :D
Answer:
look at explanation
Step-by-step explanation
The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them. This means that the force of gravity increases with mass, but decreases with increasing distance between objects.
To find the product of a 3-digit number and a 1-digit number,
you can multiply the ones, multiply the tens, multiply the
hundreds, and find the sum of each
Answer:
each number is the answer
Step-by-step explanation:
A package of 3 pairs of insulated costs $22. 47 What is the unit price of the pairs of gloves?
Answer:
7.49
Step-by-step explanation:
22.47 divided by 3
Whch of the binomials below is a factor of this trinomial x^2 + 19x + 84.
A)x-7
B)x^2+12
C)x+84
D)x+7
Answer:
The answer is D) x+7
Step-by-step explanation:
First you have to find multiples of 84 and see if they add up to equal 19.
What is the value of x?
6 (-3 -x) - 2x = 14
Answer:
x= -5 hope this helps
Step-by-step explanation:
did the math
