1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
belka [17]
3 years ago
5

Look PLZ,PLZ,PLZ help with this. I have no idea how to do this

Mathematics
1 answer:
scoray [572]3 years ago
8 0

Answer:

i know that number 4 is interceding lines because they are crossing each other

Step-by-step explanation:

You might be interested in
Linear Algebra question! Please help!
kozerog [31]

Answers:

  1. false
  2. false
  3. true
  4. false
  5. True

==================================================

Explanation:

Problem 1

This is false because the A and B should swap places. It should be (AB)^{-1} = B^{-1}A^{-1}.

The short proof is to multiply AB with its inverse (AB)^{-1}  and we get: (AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I

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 B^{-1} and the two cancel each other out.

Keep in mind matrix multiplication is <u>not</u> 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 <u>not</u> 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 A^{-1} and B^{-1} 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:

  1. If A and B are invertible, then so is AB
  2. If A and AB are invertible, then so is A*AB = A^2B
  3. If A and A^2B are invertible, then so is A*A^2B = A^3B

and 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

A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}

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 A^{-1} to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.

5 0
2 years ago
(3,4) and (-5,6) <br><img src="https://tex.z-dn.net/?f=%283%2C4%29%20and%20%28-5%2C6%29%20" id="TexFormula1" title="(3,4) and (-
IceJOKER [234]
(3,4) and (-5,6) are "coordinate planes".

These appear in algebra and math when you're graphing. These coordinate planes consist of "x" and "y" (x,y). The x's (which are 3 and -5 in your situation) should be graphed accordingly using the x-axis and the y's (which are 4 and 6 in your situation) should be graph accordingly using the y-axis. 
3 0
3 years ago
What is the value of 9 1/2​
poizon [28]

Answer:

19\2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
If you doubled the radius of a sphere, how would the volume change? A. The volume would double. B. The volume would triple. C. T
Ronch [10]
The volume of a sphere, V = (4/3)(PI)(R^3) Let k = (4/3)(PI) Therefore, V = k (R^3) Let R’ = new radius = 2R V’ =k (R’^3) = k (2R)^3 = 8 k R^3 = 8 V The volume would be eight time the original volume.
7 0
3 years ago
PLEASE HELP! POINTS!<br><br><br> Graph y =  – 4/3x + 1
9966 [12]
I'm kind of thrown off for that negative sign, but I try it out in the one that makes sense is this one [ https://gyazo.com/192a76e70d2d46979691cabbf06e6c85 ] If you can better of explain where the negative sign will be great. Hope I helped. 
4 0
3 years ago
Other questions:
  • Alyssa said if you have a two digit divisor and a three digit dividend, the person will always have two digits. If she correct?
    13·1 answer
  • Write three ratios equivalent to this:18 right handed students for every 4 left handed?
    10·2 answers
  • What is the mode for the data set?
    5·1 answer
  • Simplify <br><br> ab + ab - bc - ab + bc
    12·1 answer
  • I need help asap plz I will mark branlist
    10·1 answer
  • In isosceles △abc the segment bd (with d∈ ac ) is the median to the base ac . Find bd, if the perimeter of △abc is 50 meters, an
    7·1 answer
  • A triangular sail on a sailboat is 6meter across the bottom and 10 meters tall.
    14·2 answers
  • I have a homework question where I have to estimate the number of dentists in the UK. There is roughly 65,000 people in the UK a
    14·1 answer
  • Find the volume of the composite shape to the right to the nearest while number
    6·1 answer
  • 12(-5z - 4)<br> please help me
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!