Linear algebra, DUE IN 10 HOURS. matlab knowledge

As a convenience, this answer template is provided if you wish to easily submit your work. Be sure to save it as a PDF before submitting online! Only one submission is allowed.

Question 1: Find the inverse of .

Question 1: The inverse is:

The MATLAB code used is:

Question 2: Verify the identity: for ,

Which of these gives the zero matrix?

i. inv(A*B) - inv(A) * inv(B)

ii. inv(A*B) - inv(B) * inv(A)

Question 2: Which of the two lines of code gives the zero matrix?

For what values of a and b does the order not matter?

Questions 3-4: Find the inverse of the matrix by reducing the block matrix .

Questions 3-4: Paste in all your code for this problem here.

The inverse of A is:

Question 5: Checkerboard plot of a matrix and its inverse.

Replace the plot below with your completed plot showing both A and A–1.

Question 6: The Adjoint Formula for the Inverse

Find the inverse of the matrix using the adjoint() and det() commands.

Recall the adjoint formula:

Question 6:

The determinant of B is:

The adjoint of B is:

Question 7: A system of five equations for five unknowns has a unique solution. Find it !

Question 7: Write out the solution.

The unique solution is:

(A few of the components are given so you can check your work.)

Question 8: Cramer's Rule inside a for loop: Paste in your code to complete this for loop.

See missing steps 1, 2, 3.

clear, clc

A = [2 0 0 1 3; -2 0 1 2 -2; -5 0 0 -3 4; 5 1 0 -5 1; 2 1 4 -4 2];

b = [9;-3;0;3;7];

dA = det(A) % Use this in your for loop below.

% The body of the for loop is missing below. Complete the missing three steps.

for i = 1:5

% 1. <- Make a copy of A and name it Ai.

% 2. <- Replace column i of Ai with b

% 3. Find the ith unknown x(1,i) using Cramer's formula.

end

x % Prints out the solution

Questions 9-10: Cryptographic Example:

Questions 9 and 10:

a. Show the line of code you fixed using the round() command. Just show the one line.

>>

b. Decode the following secret message, and paste in what it says!

coded_message =

75 251 28 134 249 -59 106 268 124 16 79 -33

264 404 163 349 396 148 321 400 333 157 309 171

262 469 161 361 463 70 317 484 343 149 291 103

The secret message says:

When your lab is complete, be sure to submit it as a PDF by the due date – this Thursday before 11:59PM. You have one more day, to submit the lab (but with a small penalty), and then the window closes for good and your grade will be zero. Only one submission is allowed per student.

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