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
Anton [14]
3 years ago
15

solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of Albert Einstein, "Everything

should be made as simple as possible, but not simpler") Assume that all matrices are invertible. a.XA-1 = A3b. AXB = (BA)2 c.(A-1 X)-1 = (AB-1)-1(AB2) d.ABXA-1 B-1 =1 + A
Mathematics
1 answer:
vova2212 [387]3 years ago
7 0

a.

XA^{-1}=A^3

(XA^{-1})A=A^3A

X(A^{-1}A)=A^4

X=A^4

b.

AXB=(BA)^2

A^{-1}(AXB)B^{-1}=A^{-1}(BA)^2B^{-1}

(A^{-1}A)X(BB^{-1})=A^{-1}(BA)^2B^{-1}

X=A^{-1}(BA)^2B^{-1}

c.

(A^{-1}X)^{-1}=(AB^{-1})^{-1}(AB^2)

X^{-1}A=(BA^{-1})(AB^2)

X^{-1}A=B(A^{-1}A)B^2

X^{-1}A=B^3

(XX^{-1})A=XB^3

XB^3=A

X(B^3(B^3)^{-1})=A(B^3)^{-1}

X=A(B^3)^{-1}

d. Not totally sure what the equation is supposed to be, but I guess it's

ABXA^{-1}B^{-1}=A

ABX(BA)^{-1}=A

((AB)^{-1}(AB))X((BA)^{-1}(BA))=(AB)^{-1}A(BA)

X=(AB)^{-1}A(BA)

X=(B^{-1}A^{-1})A(BA)

X=B^{-1}(A^{-1}A)(BA)

X=(B^{-1}B)A

X=A

You might be interested in
How many solutions does the system of equations have?<br> 6x+y=2<br> -18x+3y=12
Tamiku [17]
There will be one solution. To solve that:
1. Get the y alone by switching the places.
6x+y=2 > y=2-6x 
-18x+3y=12 > 3y=12-18x > Then divide 3 on each number > y=4-6x
After doing that, you can solve this in graphing or algebra way.

Ima do the algebra way: 

SO we have 2 system of equations. Now pick one equestion.
I will pick, y=2-6x. Now Ima replace the Y with the other equation y=4-6x >  
4-6x=2-6x.

Now solve. And get >  0 aka Infinite Solution.
6 0
3 years ago
Read 2 more answers
What is 7 1/2 divided 3/4
frosja888 [35]

Answer:

10

Step-by-step explanation:

4 0
3 years ago
Given the triangle below, what is mA, rounded to the nearest tenth?
Katen [24]

Answer:

A. 24.2°

Step-by-step explanation:

I'm correct if I'm rwong

7 0
3 years ago
How would you write an equation for a non proportional table????
Bad White [126]

Answer:

i need the table

Step-by-step explanation:

But usually it has something to do with an exponent

8 0
3 years ago
How to simplify 6 to the power of -1 over -8 to the power of 0
neonofarm [45]

Answer:

\frac{1}{6}

-8 to the power of 0 = 1

(Anything to the power of 0 = 1)

and 6 to the power of -1 = 1/6

( Any number to the power of a negative number will become a fraction)

Example.

5^{ - 3}  =  \frac{1}{5^{3} }

So is will be 1/6 over 1

Which gives you your final answer.

4 0
2 years ago
Other questions:
  • Sara bought shoes for $39.95 and x pairs of socks for $1.99 each. Which expression shows the total money spent? (5 points)
    10·2 answers
  • Find the interquartile range for a data set having the five-number summary: 4.9, 12.4, 20.5, 28.8, 34.3
    8·1 answer
  • Explain the steps when solving this. <br> 10 + h &gt; 2 + 2h
    6·2 answers
  • Solve for x: |x| - 8 = - 5
    12·1 answer
  • How can the numbers 3 7 12 2 make 11​
    13·2 answers
  • What is the correct order of these numbers ... 5/6, 12/13, 0.8
    6·2 answers
  • Please someone help ASAP it’s timed
    10·1 answer
  • The sophomore class needs a combined total of 216 medium and large t-shirts for field day. The number of medium t-shirts needed
    11·1 answer
  • Pls help ! I’ll give you brainliest
    13·1 answer
  • Giving brainliest!! thanks in advance!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!