USING MATLAB to SOLVE 1. Gcnerate a random matrix A of size 3×3, with random int

Question

USING MATLAB to SOLVE

1. Gcnerate a random matrix A of size 3×3, with random integers between 0 and 2, Compute det A, det (2A), and det (10A) (you will need to use randi for this). Display your solution using the MATLAB function disp. What can you conclude about det(cA), when A is n x n and c is a scalar? 2. Generate two random 5 × 5 matrices A and B (you may use either rand or rand), and compute det (A B) and det(A) det(B Display your answers using the MATLAB function disp. Is it true in general that det(A B)-det A+det B? 3. Generate two randon 5 × 5 matrices A and B (you may use either rand or rand), and compute det(AB) and (det A) (det B). Display your answers using the MATLAB func- tion disp. Is t true in general that det(AB) -(det A) (det B)? 4·Generate a random 5 × 5 matrix A using the rand function (do not choose rand! this time For cach case, compute det A and det A-1, and the number Display answers using the MATLAB function disp. What is your conclusion based on these calcu- lations? 5. What is the rank of A? What is the det of A? Solve Ax-b by implementing Cramer's rule in MATLAB, where 3 2 4 0 0 0 4 2--3 0 2 3

Explanation / Answer

As per Chegg policy, we are supposed to answer only first complete question. So request you post others separately. Thank you.

Answer 1:
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A = randi([0, 2], 3) %generate a 3x3 matrix with values in range 0-2
disp(det(A));
disp(det(2*A));
disp(det(10*A));

sample output(can be different for you since its random)
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A =

0 2 1
0 2 2
2 0 2

4
32
4000

Conclusion:
============
From the output, we can conclude that for a scalar c and an nxn matrix A, det(cA) = c^n * det(A)

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