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
In-s [12.5K]
4 years ago
13

If A,B are n×n matrices, then (A + B)^2 = A^2 + 2AB + B^2. Either prove that this statement is true, or explain why it is false.

Mathematics
1 answer:
bonufazy [111]4 years ago
6 0
<h2>Answer:</h2>
  • The given statement is false.
  • The statement is necessarily true  when two matrix A and B commute.
<h2>Step-by-step explanation:</h2>

This statement is false.

Since, for two matrices A and B , the expansion of the term:

(A+B)^2 is given by:

(A+B)^2=(A+B)(A+B)\\\\i.e.\\\\(A+B)^2=A^2+B\cdot A+A\cdot B+B^2

Also, we know that when two matrix A and B commute then we have:

A\cdot B=B\cdot A

Hence, we get the expression as:

(A+B)^2=A^2+2A\cdot B+B^2

But when two matrix A and B do not commute then we need not have:

  (A+B)^2=A^2+2A\cdot B+B^2

You might be interested in
Write 2 equivalent expressions that illustrate the associative property of addition
Katen [24]
(5 + 2) + 1 = 5 + (2 + 1)
6 0
4 years ago
I WILL GIVE BRAINLIEST!! PLEASE HURRY
crimeas [40]

Answer:

B. It rejects the concept of social class in the American system.

Explanation:

The Enlightenment of the American Colonies was a period in time where the people were encouraged to become their own nation. This period was represented by many speeches and pieces of writing that boasted freedom of speech, equality, freedom of the press, and religious tolerance.

This specific piece of writing focuses on the aspect of all people in the nation of America having protected freedoms and rights to become their own people.

5 0
3 years ago
What is the value of L-1.1)?<br> O —2<br> 0 -1<br> 0<br> O 1
Kazeer [188]

Answer:

I do not understand.

Step-by-step explanation:

Please add a picture of explain what it is you want help with.

At this moment I do not understand the question, I am sorry.

7 0
3 years ago
Read 2 more answers
The figure below shows segments KL and MN which intersect at point P. Segment KM is parallel to segment LN:
DerKrebs [107]

Answer:

Angle KMP is congruent to angle LNP because they are alternate interior angles.

Step-by-step explanation:

Alternate interior angles are angles inside the parallel lines and on opposite sides of the transversal.

KM and NL are parallel to one another.  KMP and LNP both fall between the parallel lines; this makes them interior.

KL is a transversal for the two parallel lines.  KMP and LNP are on opposite sides of the transversal; this makes them alternate.

Therefore they are alternate interior angles.

3 0
3 years ago
Read 2 more answers
50 POINTS
Alexus [3.1K]

Answer:

105

Step-by-step explanation:

180-75=105

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is 0.68 in expanded form
    8·2 answers
  • The surface area of the square is 16 square inches. Find the value of x
    8·1 answer
  • an amusement park reported 354,605 visitors last summer what is this number rounded to the nearest thousand
    9·1 answer
  • If 2x = 14 then x=7​
    11·2 answers
  • Whats equivalent to 11 to the 8th power over 11 to the 3rd power
    7·1 answer
  • Help me..................... i neeed it
    7·2 answers
  • Graph the line with slope 3/4<br> passing through the point (5, -2).
    11·2 answers
  • A farmer sells 6.3 kg of apples and pears at the farmers .2/5 of this weight is apples and the rest is pears. How many kg of pea
    12·1 answer
  • Which of the following would be in the solution set to the system of inequalities given below?
    13·1 answer
  • A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!