Question: 1. Using MATLAB compute the determinant of Rt = for various choices of t. Comment on your results. Now compute the determinant by hand

1. Using MATLAB compute the determinant of Rt = for various choices

1. Using MATLAB compute the determinant of Rt = for various choices of t. Comment on your results. Now compute the determinant by hand for an arbitrary t. How does the theoretical result compare with your calculations? Now, using MATLAB compute Re(R) and (Rt)TR for various choices of t. By hand, compute the theoretical values of the aforementioned products for an arbitrary t. What conclusions can you infer from these results. Is the above matrix orthogonal? (a) det(A) and det (AT) (b) det(A + B) and det(A) + det (B) (c) det(AB) and det(A) det (B) cost sint sint cost 2. Compose several random 5 x 5 matrices with integer entries and use MATLAB to compute each of the following pairs of values and comment on your results. If the pairs of values do not equal in general, provide a small counter example. 1 3. Let A be a square matrice with real entries. Using the multiplicative property of determinants we have that det(A) = (det A)", where n 1 and integer. Consider the matrix 0.03 0.001 0 1 0 0 A = 0.23 0 0.04 Using MATLAB compute det (A), det (A00), and det(A150) and based off this information state whether the matrices A, A100, and A150 are invertible. Do these results agree with the multiplicative property of determinants? Comment on your results and explain any differences.

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