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
liberstina [14]
2 years ago
5

[ MATLAB] Check some linear algebra rules: Enter the following matrices:

Mathematics
1 answer:
lana66690 [7]2 years ago
3 0

Answer:

Step by step explanation along with Matlab code and output is provided below.

Step-by-step explanation:

We are given three matrices A, B, and C of size 2x2

A = [0 1; 0 0]

B =[1 2; -3 -6]

C =[4 -2; -2 1]

Output:

A =  0     1

     0     0

B =  1     2

    -3    -6

C =   4    -2

    -2     1

Let us first check if the given matrices A, B, and C are singular or not

% the Matlab function det( ) calculates the determinant of a matrix

det_A=det(A)

det_B=det(B)

det_C=det(C)

Output:

det_A =  0

det_B =  3.3307e-16  (its practically zero)

det_C =  0

So the given matrices are singular which means that the determinant of the matrix is zero so inverse of these matrices is not possible.

Rule I:

a1=B*C

Output:

a1 =  0     0

      0     0

In Matrix theory, if BC=0 then B=0 or C=0 doesn't hold true

For matrices B*C=0 does not imply that either B or C is zero matrix but rather it implies that at least one of them is singular. In this case we know that both B and C are singular matrices therefore, BC=0  

Rule II:

a2=A^2

Output:

a2=  0     0

      0     0

In Matrix theory, if A^2=0 then A=0 doesn't hold true

For matrices A^2=0 does not imply that A is zero matrix but rather it implies that A is singular. We already know that A is singular therefore, A^2=0

Rule III:

a3_L=(A+B)^2

a3_R=A^2+2*A*B+B^2

Output:

a3_L =    -8   -15

            15    27

a3_R =   -11   -22

             15    30

In Matrix theory, (A + B)^2 = A^2 + 2AB + B^2 doesn't hold true.

(A + B)^2 = A^2 + 2AB + B^2 might hold true if AB = BA,  but generally, AB≠BA in matrix algebra.

Rule IV:  

a4_L=(A-B)*(A+B)

a4_R=A^2-B^2

Output:

a4_L =     2     3

            -15   -27

a4_R =    5    10

            -15   -30

In Matrix theory, (A-B)(A+B)  = A^2-B^2  doesn't hold true.

Rule V:    

a5_L=A*(B+C)

a5_R=A*B+A*C

Output:

a5_L =    -5    -5

              0     0

a5_R =   -5    -5

              0     0

In Matrix theory, A(B+C) =  AB+AC  holds true.

Rule VI:    

a6_L=A*(B+C)

a6_R=B*A+C*A

Output:

a6_L =    -5    -5

              0     0

a6_R =    0     5

              0    -5

In Matrix theory, A(B+C) =  BA+CA  doesn't hold true.

on a side note;  (B+C)A =  BA+CA holds true

Rule VII:  

a7_L=(A*B)^2

a7_R=A^2*B^2

Output:

a7_L =     9    18

              0     0

a7_R =     0     0

              0     0

In Matrix theory, (AB)^2  =A^2*B^2   doesn't hold true.

(AB)^2  =A^2*B^2   might hold true if and only if  BA=AB  which is not true in general.  

You might be interested in
What is the area of the shaded region?
kotegsom [21]

Answer:

Step-by-step explanation:

(7*11)-(22/7*2^2)

77-(22/7*4)

77-88/7

77-12.57

64.43

3 0
2 years ago
Kesha wants to know whether x + 4 is a factor of p(x) = −3x^3 − 15x^2 − 16x −16.
Reika [66]
It's the factor theorem.
P(-4)
Equal to 0
3 0
3 years ago
A cars velocity on a straight highway increases uniformly from 20km/h to 70km/h in 0.008h. Find the acceleration in km/h2
Bess [88]

Answer:

a = 70 km/h - 20 km/h / 0.008 h  = 50 km/h / 0.008 h  = 6250 km/h²

3 0
2 years ago
Read 2 more answers
Given that angle a = 54° and angle b = 48°, work out x.
Arisa [49]
If it’s a triangle then it has to equal 180
so 48+54+x=180
48+54=102
180-102=x

x=78
3 0
2 years ago
The volume of the rectangular prism picture included
lbvjy [14]
88in·cubic is it alright
6 0
3 years ago
Other questions:
  • Paper clips are sold in boxes of 1000.
    13·1 answer
  • Can the law of sines be used to solve the triangle
    8·1 answer
  • What is 66 over 108 in the lowest term
    15·2 answers
  • Select a point that is a solution to the system of inequalities
    6·2 answers
  • The measure of minor arc JL is 60°.
    15·2 answers
  • NEED TO SHOW ALL WORK) For each of the equations given below, use the triangle method to solve for the
    6·1 answer
  • Billy is going on a road trip. The amount of gas g (in gallons) left in his tank varies inversely with the amount
    9·1 answer
  • PLEASE HELP, MARKING BRAINLIEST!!!!
    13·1 answer
  • Tell whether the angles are adjacent or vertical. Then find the value of x. The angles are . Question 2 x=
    8·1 answer
  • Please help! 20 points thanks :)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!