The matrices C, D, F, and G are symmetric while matrix H is skew-symmetric and matrix E is non-symmetric.
A matrix is an array of elements(numbers) in a peculiar order. A matrix with m rows and n columns is said to be of order m × n.
As it is known that [tex](A + B)^t = A^t + B^t[/tex] and [tex](AB)^t = B^t A^t[/tex] for any n × n matrices A and B.
Also, if matrices A and B are symmetric, then
[tex]A^t = A[/tex] and [tex]B^t = B[/tex].
a) Given that
C = A + B
Take the transpose of matrix C,
[tex]C^t = (A + B)^t[/tex]
[tex]= A^t + B^t \\= A + B = C[/tex].
Hence, matrix C is symmetric.
b) Given that
D = A²
Take the transpose of matrix D,
[tex]D = (A^2)^t[/tex]
[tex]= (AA)^t \\= A^t A^t \\= AA \\= A^2 = D[/tex].
Hence, matrix D is symmetric.
c) Given that
E = AB
Let's take an example,
A = [tex]\left[\begin{array}{cc}1&2&2&1\end{array}\right][/tex] and
B = [tex]\left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right][/tex]
So,
E = AB
[tex]=\left[\begin{array}{cc}1&2&2&1\end{array}\right] \times \left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right]\\= \left[\begin{array}{cc}-1&3&1&0\end{array}\right][/tex]
Clearly, matrix E is non-symmetric.
d) Given that
F = ABA
Take the transpose of matrix F,
[tex]F^t = (ABA)^t[/tex]
[tex]= A^t B^t A^t\\ = ABA = F[/tex].
Hence, matrix F is symmetric.
e) Given that
G = AB + BA
Take the transpose of matrix G,
[tex]G^t = (AB + BA)^t[/tex]
[tex]= (AB)^t + (BA)^t \\= B^t A^t + A^t B^t \\= BA + AB = G[/tex].
Hence, matrix G is symmetric.
f) Given that
H = AB-BA
Take the transpose of matrix H,
[tex]H^t = (AB - BA)^t[/tex]
[tex]= (AB)^t - (BA)^t \\= B^t A^t - A^t B^t \\= BA - AB = -H[/tex].
Hence, matrix H is skew-symmetric.
Thus, the matrices C, D, F, and G are symmetric while the rest are not.
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Which of the following numbers can be expressed as repeating decimals? 4 over 7, 2 over 5, 7 over 8, 4 over 9
Answer:
4 over 9
Step-by-step explanation:
4 over 7 = 0.571428571
2 over 5 = 0.4
7 over 8 = 0.875
4 over 9 = 0.444444444444444
Answer:
4/7 and 4/9
Step-by-step explanation:
1/16,16/100,1/6,1/3 which is equivalent to this decimal 0.16 (6 repeating)?
Answer:
1/6
Step-by-step explanation:
I need help to find the slope between these two points
Answer:
11/2
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1}}[/tex]
what is 7 × 5 + (3 × 5)
7 x 5 + (3 x 5) First do the parenthesis
7 x 5 + 15 Next do multiplication (left to right)
35 + 15 Last add the two remaining numbers
50
Answer : 50
Given:
p: Two linear functions have different coefficients of x.
q: The graphs of two functions intersect at exactly one point.
Which statement is logically equivalent to q-p?
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one
point.
O If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect
at exactly one point.
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same
coefficients of x.
O If the graphs of two functions intersect at exactly one point, then the two linear functions have the same
coefficients of x.
Answer:
Linear function A and linear function B both have the same input values as shown below. Why will the output values for linear function A always be different than the corresponding output values for linear function B? The initial values of the two functions are different, and the rates of change of the two functions are also different. The initial values of the two functions are different, and the rates of change of the two functions are the same. The initial values of the two functions are the same, and the rates of change of the two functions are different. The initial values of the two functions are the same, and the rates of change of the two functions are also the same.
I need help PLEASE help mel
Answer:
A) The first checkbox
B) The first and third checkbox
Step-by-step explanation:
A) [tex]\frac{-5}{-4}[/tex] ⇒ the negative would cancel/cross out and leave you with [tex]\frac{5}{4}[/tex]
B) Look for one negative sign in either the numerator or denominator.
if I eat 230 gumballs and there was a total of 1696 and my friend takes the rest of the 1760 gumballs. how did we get 1760 if there was 1696 and I ate 230. how many gumballs was added?
294 gumballs were added because if u subtract 230 from 1696 you get 1466 which was the number you had when you are 230 gumballs so you take 1466 and subtract it from 1760 you get the amount of gumballs that was added.
just like this other lady said 294 gumballs were added
Which of the following expressions are equivalent? Justify your reasoning,
А. 4 √x^3
B. 1/ x^-1
C. 10 √x^5 times x^4 times x^2
D. X1/3 times x^1/3 times x^1/3
Answer:
B and D
Step-by-step explanation:
B:
Anything to a negative power means that it is 1/that to the positive power.
E.g. x^-1 = 1/x^1
In other words, anything to the power of a negative switches sides of a fraction (i.e. if in numerator moves to denominator and vice versa.)
1/x^-1 = 1/1/x^1 which is just equal to x, because there are x number of 1/xs in one (1/x * x =1) Therefore Option B is equal to just x.
D: (assuming the first given term is x^1/3 and not X1/3 (?) Correct me if I'm wrong).
x^1/3 * x^1/3 * x^1/3 is also equal to just x.
This is because when multiplying together terms with the same base (x in this case) the exponents just add together, so:
x^1/3 * x^1/3 * x^1/3 = x^(1/3 +1/3 +1/3) = x^1 = x.
Therefore B and D are equivalent because they both equal x.
Hope this helped!
A candidate scored 32 marks out of 80.find his percentage score
Answer:
40%
Step-by-step explanation:
Take the amount over the total
32/80
.4
Change to percent form by multiplying by 100
40 %
Name the position held by the digit 5 in each numeral.
a. 952
b. 5,432
c. 115
d. 50,768
e. 113,598
f. 5,027,649
Answer:
a. 952= 50 or tens
b. 5,432= 5000 or thousands
c. 115= 5 or ones
d. 59,768= 50000 or tens of thousands
e. 1113,598= 500 or hundreds
f.5,027,649= 5000000 or million
The table shows the values of two quantities for an astronaut on Earth and Earth's moon. Which of the following names the quantity and correctly explains why that represents the astronaut's mass? Quantity A, because it remains the same throughout Quantity B, because it is independent of other quantities Quantity B, because it changes with gravitational strength Quantity A, because it measures the force acting on the astronaut
Answer:
A.
Step-by-step explanation:
the answer is A. because in space, the whole thing is the same amount of density. except for the sun but the question says earth and moon. hop this helps!!! please give me brainliest answer!!!
Quantity A because it changes with gravitational pull.
Given that, the Astronaut's mass of quantity A on earth is 70 units and on the moon is 70 units.
The Astronaut's mass of quantity B on earth is 686 units and on the moon is 112 units.
What happens to an astronaut's mass in space?We can measure weight here on Earth, but not in the microgravity environment on the International Space Station. Mass plays a critical role in the activities and experiments performed by the astronauts. Mass does not change whether it is measured on Earth or the ISS.
Now, mass defines the constitutive matter of an object. It is immutable (does not change). Although it could be converted into energy, the matter is constant.
On the other hand, the weight of an object (gravitational force) depends on the acceleration due to gravity.
That is why an astronaut weighs about three times more on earth than on Mars. The gravitational acceleration on Mars is about one-third that on earth.
Therefore, Quantity A because it changes with gravitational pull.
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Aaron is 53 ž inches tall. His friend Xaviar was 48.75 inches tall, but grew 2 inches over
the summer. How much taller is Aaron than Xaviar?
Answer:
2..25
Step-by-step explanation:
m3 = 64
What’s the value of m
Answer:
m =64/3
Step-by-step explanation:
m=21 1/3 m=21.3
Least to greatest is the same as ascending order or descending order?
Answer:
It is the same as ascending order
Step-by-step explanation:
It is the same as ascending order becuase Least is small and Greatest is big so you are going upwards.
Hope This Helps :)
Answer:
Ascedning order
Step-by-step explanation:
Decend typically means "go down", in this case greatest to least goes from the biggest number to the smallest ( go down from biggest to smallest). Ascending means to "rise" or "go up", so to starts at the smallest value ascedning to the biggest value.
least to greatest = ascending
greatest to least = descending
If you travel 70000 M at a rate of 25 m/s and , how long does it take to complete the trip?
Answer:
Time=2800 seconds.
Time in minutes= 46.67 minutes
Time in hours= 0.778 hours
Step-by-step explanation:
Distance traveled= 70000 m
Rate or speed of travel= 25m/s
To calculate the time for the travel, we multiply the rate of travel by the distance covered or traveled.
Rate= distance/time
Time= distance/rate
Time= 70000/25
Time=2800 seconds.
Time in minutes= 2800/60
Time in minutes= 46.67 minutes
Time in hours = 2800/(60*60)
Time in hours= 2800/360
Time in hours= 0.778 hours
(5x third power) (4x third power)
Answer:
Step-by-step explanation:
(5x³)(4x³) = 20x^6
Solve the equation for a 62=a(25-0)(25-50)
A function is described by the following ordered pairs: (7, 4.5) (–4, 7.2) (–7.2, –4) (5.2, 3) Which set of ordered pairs represents the inverse of the function? (7, –4), (–7.2, –4), (3, 5.2), (4.5, –4) (7, –4), (–7.2, 5.2), (4.5, 7.2), (–4, 3) (4.5, 7), (7.2, –4), (–4, –7.2), (3, 5.2) (7, 4.5), (–4, 7.2), (–7.2, –4), (5.2, 3
Answer: the third answer
Step-by-step explanation:
did it online right now
Answer:
It is C.
Step-by-step explanation:
I got it correct on Edg.
If the measure of angle ABD is 100, what is the measure of angle ABC
i dont know. Im sorry about that.
what is the simplified form of this expression? sqrt ((1764x^20)/(36x^4))
assume x =/ 0
Answer:
{x!=0, sqrt((1764 x^20)/(36 x^4))} = {x!=0, 7 sqrt(x^16)} thus: 7x^16
Step-by-step explanation:
Solve for x
4r – 9 – 6x = 21
Answer:
X= 30-4r/-6
Step-by-step explanation:
1. Move the 9 to the other side. (21+9=30)
2. subtract the 4r and move it to the other side (-6x=21-4r)
3. divide both sides by -6
Write an equation in slope-intercept form for the line that passes through the point ( 2 , 3 ) and is perpendicular to the line − 5 x + 4 y = − 3 .
The slope of a line in standard equation will be [tex]\frac{-A}{B}[/tex]
[tex]m=\frac{5}{4}[/tex]
The slope of a perpendicular line to this line will be opposite and reciprocal.
[tex]m=-\frac{4}{5}[/tex]
Then, we can plug in the point given to get the [tex]b[/tex] value.
[tex]3=-\frac{4}{5}(2)+b[/tex]
[tex]3=-\frac{8}{5}+b[/tex]
[tex]b=\frac{23}{5}[/tex]
[tex]y=-\frac{4}{5}x+\frac{23}{5}[/tex]
Hope this helps.
頑張って!
What is the greatest common factor of 20 and 36?
Answer:
4
Step-by-step explanation:
i did math
Answer: 4
Step-by-step explanation:
The Greatest common factor is the largest factor that both numbers share, so find their factors,
Factors of 20: 1,2,4,5,10 and 20
Factors of 36: 1,2,3,4,6,9,12,18, and 30
The largest factor that both numbers share is 4
How do u say 0.99999999 in words
Answer:
Zero Point Nine Nine repeating?
Step-by-step explanation:
Evaluate 5w + 1p for w = 3 and p =
- 6
Answer:
9
Step-by-step explanation:
We are given the expression:
[tex]5w+1p[/tex]
and asked to evaluate for w=3 and p= -6. Therefore, we must substitute 3 in for w and -6 in for p.
[tex]5(3)+1(-6)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
Multiply 5 and 3.
⇒ 5*3=15
[tex]15+1(-6)[/tex]
Multiply 1 and -6.
⇒1*-6= -6
[tex]15 + -6[/tex]
Add 15 and -6.
⇒ 15 + -6= 15-6= 9
[tex]9\\[/tex]
The expression 5w+1p when evaluated for w=3 and p= -6 is 9
1. Write the fraction 8/10 in simplest form.
A. 16/20
B. 2/5
C. 4/5
D. 2/10
Answer:
Step-by-step explanation:
C.
Answer:
C 4/5
Step-by-step explanation:
Divide the numerator and denominator by 2
8/2=4
10/2=5
4/5
Hope this helps :-)
V64
를
(16
4
V20
5
Which of the following is an irrational number
Answer: V20
Step-by-step explanation:
Let's go down the list, shall we?
First, V64. I am going to assume that the V is a square root. If you take the square root of 64 you would get 8, which is not an irrational number.
2/2 would be one of the easiest, its just 1 if you simplify it
(16 would be a rational number, even if you took the square root.
4 is four, a rational number
V20 is an Irrational number, again, assuming that the V is a square root symbol, and you took the square root of it, you would get 4.472135955... an infinite number without a pattern
And 5 is just five, a whole number
There are five consecutive odd integers. The sum of the three smallest is 3 more than the sum of the two largest. Find the integers. 15 points
Answer:
11 13 15 17 19
Step-by-step explanation:
We will solve this word problem using 2k+1 which is one of the general forms of an odd integer.
Let 2k+1 be the first odd integer.
(2k+1) + (2k+3) + (2k +5) = (2k+7) + (2k +9) + 3 (the +3 is to accommodate for the left side being 3 more than the right)
Solve for k
6k + 9 = 4k + 19
6k - 4k + 9 = 4k-4k + 19
2k + 9 = 19
2k + 9 - 9 = 19 - 9
2k = 10
2k/2 = 10/2
k = 5
To get the first digit in the series plug in 5 for k
2k+1
2(5) + 1
10 + 1 = 11
So our series is 11, 13, 15, 17, 19
Let's test it.
11 + 13 +15 = 39
17 + 19 = 36
So we are correct, the first 3 integers are 3 more that the sum of the last 2.
Answer:
11, 13, 15, 17, 19
Step-by-step explanation:
I am doing this in my RSM homework, just saying this is correct. I guessed and checked to do this.
Write an absolute value equation that has the solutions $x=8$ and $x=18$
Answer:
Step-by-step explanation:
Let |x-a|=b
then x-a=±b
so x-a=b
or x=a+b
so a+b=18 ...(1)
and x-a=-b
or x=a-b
or a-b=8 ...(2)
adding (1) and (2)
2a=26
a=26/2=13
subtract (2) from (1)
2b=10
b=10/2=5
|x-13|=5
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
27.
Step-by-step explanation:
If x >= 4 then f(x) = 5x - 3.
So, as 6 is greater than 4 we have
f(6) = 5(6) - 3
= 30 - 3
= 27.