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
solong [7]
3 years ago
12

Let M be the set of all nxn matrices. Define a relation on won M by A B there exists an invertible matrix P such that A = P BP S

how that is an equivalence relation.
Mathematics
1 answer:
Sophie [7]3 years ago
4 0

Answer:

Recall that a relation is an <em>equivalence relation</em> if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.

<em>Reflexive: </em>We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that A=J^{-1}AJ. Thus, A↔A.

<em>Symmetric</em>: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that A=P^{-1}BP. In this equality we can perform a right multiplication by P^{-1} and obtain AP^{-1} =P^{-1}B. Then, in the obtained equality we perform a left multiplication by P and get PAP^{-1} =B. If we write Q=P^{-1} and Q^{-1} = P we have B = Q^{-1}AQ. Thus, B↔A.

<em>Transitive</em>: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have A=P^{-1}BP and from B↔C we have B=Q^{-1}CQ. Now, if we substitute the last equality into the first one we get

A=P^{-1}Q^{-1}CQP = (P^{-1}Q^{-1})C(QP).

Recall that if P and Q are invertible, then QP is invertible and (QP)^{-1}=P^{-1}Q^{-1}. So, if we denote R=QP we obtained that

A=R^{-1}CR. Hence, A↔C.

Therefore, the relation is an <em>equivalence relation</em>.

You might be interested in
What is the domain of this graph?
Elenna [48]
A. Whole numbers from 0 to 10

The domain is composed of all x value on the graph. Every point is on a whole number for x.
7 0
3 years ago
PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!!
kenny6666 [7]

Answer:

x=7.8

Step-by-step explanation:

take 49 degree as reference angle

using cos rule

cos 49=adjacent/hypotenuse

0.65=x/12

0.65*12=x

7.8=x

3 0
3 years ago
Read 2 more answers
The little Mexican restaurant sells only two kinds of beef burritos mucho beef sandwich Lucho beef last week the restaurant orde
Finger [1]

Answer:

Cost of a single Mucho beef burrito: \$5.5

Cost of a double Mucho beef burrito: \$6.5

Step-by-step explanation:

<h3> The exercise is: "The Little Mexican restaurant sells only two kinds of beef burritos: Mucho beef and Mucho Mucho beef. Last week in the restaurant sold 16 orders of the single Mucho variety and 22 orders of the double Mucho. If the restaurant sold $231 Worth of beef burritos last week and the single neutral kind cost $1 Less than the double Mucho, how much did each type of burrito cost?"</h3>

Let be "x" the the cost in dollars of a single Mucho beef burrito and "y" the cost in dollars of a double Mucho burrito.

Set a system of equations:

\left \{ {{16x+22y=231} \atop {x=y-1}} \right.

To solve this system you can apply the Substitution Method:

1. Substitute the second equation into the first equation and solve for "y":

16(y-1)+22y=231\\\\16y-16+22y=231\\\\38y=231+16\\\\y=\frac{247}{38}\\\\y=6.5

2. Substitute the value of "y" into the second equation and evaluate in order to find the value of "x":

x=6.5-1\\\\x=5.5

5 0
3 years ago
The function y = 8.5(1.1)x models the population in thousands of a town where x is the number of years after 2000. What will be
nikdorinn [45]

Answer:

The population will be at 65.45 in 2007.

Step-by-step explanation:

I graphed the equation below to find the answer.

If this answer is correct, please make me Brainliest!

6 0
3 years ago
Write an equation and solve
erma4kov [3.2K]
10 divided by 2 minus 1 equals 4
3 0
2 years ago
Read 2 more answers
Other questions:
  • find 40% of 60 using two different strageties, one of which must include a pictorial model or digram?pls help
    15·1 answer
  • PLEASE HELP ME I AM ON A TEST . WILL MARK BRAINLIEST
    12·1 answer
  • Let the graph of f(x) represent the cost in thousands of dollars to feed the zoo animals daily, where x is the number of animals
    5·2 answers
  • Evil bunny's carrot soup calls for 5/8 cups of chopped carrots per serving. If evil bunny has chopped 7 1/2 cups of chopped carr
    12·1 answer
  • How does knowing properties of exponents
    7·1 answer
  • i lost my old brainly account name it was called official norths :( i forgot the password i will love if you help me with this p
    8·2 answers
  • If x + y = 7 and xy = 4, then find the value of x^2 + y^2.
    13·2 answers
  • I need help finishing my homework please
    14·2 answers
  • PLZ SOME ONE HELP WITH THISS
    11·1 answer
  • One positive integer is 2 less than twice another. The sum of their squares is 628. Find the integers.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!