Answer:
7 hundredths
2 tenths
Step-by-step explanation:
7 is in the hundredths place and there is no zero so then to would be in the tenths place
Linear Algebra question! Please help!
Which of the following statements are true for all invertible n x n matrices A and B?
Answers:
falsefalsetruefalseTrue==================================================
Explanation:
Problem 1
This is false because the A and B should swap places. It should be [tex](AB)^{-1} = B^{-1}A^{-1}[/tex].
The short proof is to multiply AB with its inverse [tex](AB)^{-1}[/tex] and we get: [tex](AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I[/tex]
The fact we get the identity matrix proves that we have the proper order at this point. The swap happens so that B matches up its corresponding inverse [tex]B^{-1}[/tex] and the two cancel each other out.
Keep in mind matrix multiplication is not commutative. So AB is not the same as BA.
-------------------------
Problem 2
This statement is true if and only if AB = BA
(A+B)^2 = (A+B)(A+B)
(A+B)^2 = A(A+B) + B(A+B)
(A+B)^2 = A^2 + AB + BA + B^2
(A+B)^2 = A^2 + 2AB + B^2 ... only works if AB = BA
However, in most general settings, matrix multiplication is not commutative. The order is important when multiplying most two matrices. Only for special circumstances is when AB = BA going to happen. In general, AB = BA is false which is why statement two breaks down and is false in general.
-------------------------
Problem 3
This statement is true.
If A and B are invertible, then so is AB.
This is because both [tex]A^{-1}[/tex] and [tex]B^{-1}[/tex] are known to exist (otherwise A and B wouldn't be invertible) and we can use the rule mentioned in problem 1. Make sure to swap the terms of course.
Or you can use a determinant argument to prove the claim
det(A*B) = det(A)*det(B)
Since A and B are invertible, their determinants det(A) and det(B) are nonzero which makes the right hand side nonzero. Therefore det(A*B) is nonzero and AB has an inverse.
So if we have two invertible matrices, then their product is also invertible. This idea can be scaled up to include things like A^4*B^3 being also invertible.
If you wanted, you can carefully go through it like this:
If A and B are invertible, then so is ABIf A and AB are invertible, then so is A*AB = A^2BIf A and A^2B are invertible, then so is A*A^2B = A^3Band so on until you build up to A^4*B^3. Therefore, we can conclude that A^m*B^n is also invertible. Be careful about the order of multiplying the matrices. Something like A*AB is different from AB*A, the first of which is useful while the second is not.
So this is why statement 3 is true.
-------------------------
Problem 4
This is false. Possibly a quick counter-example is to consider these two matrices
[tex]A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}[/tex]
both of which are invertible since their determinant is nonzero (recall the determinant of a diagonal matrix is simply the product along the diagonal entries). So it's not too hard to show that the determinant of each is 1, and each matrix shown is invertible.
However, adding those two mentioned matrices gets us the 2x2 zero matrix, which is a matrix of nothing but zeros. Clearly the zero matrix has determinant zero and is therefore not invertible.
There are some cases when A+B may be invertible, but it's not true in general.
-------------------------
Problem 5
This is true because each A pairs up with an [tex]A^{-1}[/tex] to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.
Finding congruent angles
Answer:
AAS
Step-by-step explanation:
There are two congruent angles, but the congruent side is not included between the two angles.
Naiomis parents want to have $50,000 saved for her college education if they invest $20,000 today and earns 7% interest compounded annually about how long would it take them to save the $50,000
Answer:
13.54 years
Step-by-step explanation:
Saw the answer to this before
Hope this helps!
passes through (1, -1) and (2,0)
Answer:
y = x - 2
Step-by-step explanation:
1. Find the slope - change in y/change in x
[tex]\frac{0-(-1)}{2-1}[/tex] = 1
Slope is 1
2. Find y-intercept
y = x + b
Substitute a point (2,0)
0 = 2 + b
b = -2
3. Put the equation together
y = x - 2
7= 4x + 7
can someone please help me solve this :,)
Answer:
Here
Step-by-step explanation:
7 = 4x + 7
Cancel out the 7's on each side by adding negative 7 to both sides...
0 = 4x
Now find how much for x alone
4x = 0
divide both sides by 4
x = 0
X = 0
7 = 0 + 7
7 = 7
A stereo marked down $75. If this is a 15% decrease, find the sale price.
Answer:
The Marked Price is 63.75
Step-by-step explanation:
15/100 * 75 = 11.25
75 - 11.25 = 63.75
Hence the Marked Price is 63.75
Arnold
25
CAR 1:
A monthly produce box is
delivered to Ms. Jones'
door. There is an initial set
up fee of $25.00 plus
$30.00 each week. If Ms.
Jones spent $265, then
how many weeks did she
receive the produce
box?
Amy
30
Answer:
5
Step-by-step explanation:
because it is the right answer
Answer:
8 weeks
Step-by-step explanation:
265-30 = 240
240/30(per week)=8
Answer is 8 weeks
how to list the first ten multiples of 7
Answer:
7,14,21,28,35,42,49,56,63,70
Step-by-step explanation:
just add 7 lol anyways here ya go :)
1.. Use long division to divide.
(2x2 + 10x + 12) = (x + 3)
Answer:
2(x+2)
Step-by-step explanation:
(2x²+10x+12)/(x+3)=(2(x²+5x+6))/(x+3)=(2(x²+2x+3x+6))/(x+3)=(2(x(x+3)+2(x+3)))/(x+3)=(2(x+3)+(x+2))/(x+3)=2(x+2)
i hope you understand (well it's math)
The average weight of the class of 35 students was 45 KG. with the admission of a new student the average weight came down to 44.5 kg. find the weight of a new student
The weight of the new student is 27 kg.
Average weight
= total weight ÷total number of students
1) Define variablesLet the total weight of the 35 students be y kg and the weight of the new student be x kg.
2) Find the total weight of the 35 students[tex]45 = \frac{y}{35} [/tex]
y= 35(45)
y= 1575 kg
3) Write an expression for average weight of students after the addition of the new studentNew total number of students
= 35 +1
= 36
Total weight
= total weight of 35 students +weight of new students
= y +x
[tex]44.5 = \frac{y + x}{36} [/tex]
4) Substitute the value of y[tex]44.5 = \frac{1575 + x}{36} [/tex]
5) Solve for x36(44.5)= 1575 +x
1602= x +1575
Subtract 1575 from both sides:
x= 1602 -1575
x= 27
Thus, the weight of the new student is 27 kg.
Does translating a figure can change the side length
Answer:
No.
Step-by-step explanation:
Translation is a type of rigid transformation. It simply moves the figure around the coordinate plane, so the size doesn't change.
Need help so much on Circle
Please help me for my geometry honors work please! Thank you
Answer:
x = 95
Step-by-step explanation:
The total degree of a circle is 360. The twp arcs on each side of the parallel lines are equal.
Subtract 135 and 35 from your total
360 - 135 - 35 = 190
Divide your answer by 2
190 ÷ 2 = 95
Which lunch box holds more? 3.75 in. 7.5 in. 10 in. or 3.75 in. 8 in. 9.5 in.
They are both really the same. so they should hold the same. All that happened is one moved a 1/2 inch over to the length from the height.
c or b???????????????
Answer:
i think it's b4
Step-by-step explanation:
Calculate the arithmetic mean of the numbers.
-121 and 49
Answer: -72 I think
Step-by-step explanation:
Hope this helps :)
Graph the line using a point and a slope. Write the equation of each line.
a line that passes through the point (0, –3) and parallels to another line whose slope is
1.2.
Answer:
y=1.2x-3
Step-by-step explanation:
I had this as an rsm problem a few weeks ago and forgot how to solve it lol hope this helps
Please help if you can.
Answer:
C
Step-by-step explanation:
Exponent Rule of algebra
New volume of cube
Please help me
Answer:
above me is maybe a yes or no
Step-by-step explanation:
brainlles to above me
A triangle has sides with lengths of 13 feet, 16 feet, and 4 feet. Is it a right triangle?
well, a right-triangle will have one angle that is 90°, and using the pythagorean theorem, we also know that the longest side is really the root of the sum of the square of the other two. After all that mouthfull let's check
[tex]\stackrel{longest}{16}~~ = ~~\sqrt{\underset{short}{13^2}~~ + ~~\underset{short}{4^2}}\implies 16=\sqrt{169+16} \\\\\\ 16=\sqrt{185}\implies 16^2=185\implies 256~~ \ne ~~185\qquad \leftarrow \textit{nope, it isn't}[/tex]
Can someone plz help
Answer:
9. answer: -3, 10. answer: 5
40 - [(8 x 7) - (5 x 6)] need the work also
[tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]
______________________________
[tex]\bold{Solution~Steps:}[/tex]
[tex]1.)~Multiply~the~parenthesis:[/tex]
[tex]\bold{8}[/tex] × [tex]\bold{7=56}[/tex][tex]\bold{5}[/tex] × [tex]\bold{6=30}[/tex][tex]2.)~Subtract~the~parenthesis:[/tex]
[tex]\bold{[56-30]=26}[/tex][tex]\bold{When~there~are~2~sets~of~parentheis~you~have~to~solve~according~to~order.}[/tex][tex]3.)~Subtract~on~the~side~without~an~equal:[/tex]
[tex]\bold{40-26=14}[/tex][tex]\bold{14=14}[/tex]______________________________
[tex]\bold{Answer:}[/tex]
[tex]\bold{The~exact~form~of~this~expression~is~\boxed{14=14}}[/tex]______________________________
[tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~-TotallyNotTrillex}[/tex]
Find three consecutive even integers whose sum is -48.
Answer:
48 then it would be 32? im not sure that what i caculated
Step-by-step explanation:
8-9(x+1) = ax+4
In the equation shown above a is the constant ?
Determine the slope of the line that passes through the given points. Complete your work in the space provided
(8,1)and (8,-4)
Answer:
undefined
Step-by-step explanation:
(y2-y1)/(x2-x1)
replacing x and y with the given value:
(-4-1)/(8-8)
-5/0
the slope is undefined because the run is 0
The sum of the 6th and seventh terms in a sequence of 12 numbers with a common difference is 16. What is the Sum of the number sequence
Answer:
96
Step-by-step explanation:
commom difference = d
a₆ + a₇ = 16
a₅ + a₈ = (a₆ - d) + (a₇ + d) = a₆ + a₇ = 16
a₄ + a₉ = (a₆ - 2d) + (a₇ + 2d) = a₆ + a₇ = 16
Similarly,
a₃ + a₁₀ = 16, a₂ + a₁₁ = 16, a₁ + a₁₂ = 16
so
a₁ + a₂ + ... + a₁₁ + a₁₂ = 6 x 16 = 96
class 6 students come here I will give you notes class is started come here fast I am waiting come with your name and class girls come fast
Answer:
1+x it means I plus the rest
8. Which set of numbers is arranged in increasing order?
A 23 873. 24 765,25 000.5 678)
B. (16 287. 16 728.16 827, 16 872
C. 98 782.98 728.98 287.98 278)
D. 78 082.78 802.78 208.78 028)
Answer:
its B :)
Step-by-step explanation:
i took the test
The school band has 115 members. They are raising money for band camp.
If each member raises $75, what is the total amount of money raised for band camp?
A. $8,625
B. $7,750
C. $8,605
D. $8,305
3
4
A group of volunteers packed 198 bags of rice. Each bag contained 3
kilo of rice. How many kilograms of rice did the volunteers pack?
Answer:
No. of bags of rice packed = 198
Amount of rice in each bag = 3 kg
Therefore, total kilograms of rice packed=198×3=594 kg
Step-by-step explanation:
Hope this helps you
Do mark me as brainliest
They packed 594 kilograms of rice.
Given:
Number of bags packed by the group of volunteers = 198
Number of kilo a bag contains = 3 kg
Therefore:
Number of kilograms of rice packed by the volunteers = number of bags packed [tex]\times[/tex] number of kilo one bag of rice weighs
Thus:
Number of kilos of rice packed = [tex]198 \times 3 $ kg\\[/tex]
[tex]= 594 $ kg[/tex]
Therefore, the volunteers packed 594 kilograms of rice.
Learn more here:
https://brainly.com/question/21146374
the diagonals of a square ___ each other, are ___ to each other, ___ opposite angles and are ___
Step-by-step explanation:
The diagonals of a square bisect each other, are perpendicular to each other, bisect opposite angles and are congruent.