![]() ![]() ![]() Normalize the first row of R to get R ( 1, 1 ) = 1 : R = A R ( 1, i ) = R ( 1, i ) / R ( 1, 1 ) (note the use of the colon to operate on whole rows of the matrix). (Do not include this part in your lab write-up.) (a) Generate a 3 × 4 matrix A with random integer entries by the command A = f i x ( 1 0 ∘ rand ( 3, 4 ) ) To transform A into R = rref ( A ), start with R = A. Since rref (A) is uniquely determined by A, this does not affect the final answer. In this demonstration, each pivot is chosen to be the largest in its column (for numerical stability), so extra row interchanges are used. You will see a step-by-step example of the row operations that transform a matrix A into its reduced row echelon form R = rref ( A ). n, and save the result (you will need to do this in future labs also). Insert the name of the directory where you have copied the Tcode rrefmovie. If you get an error message ? Undefined function or variable rrefmovie, click on Set Path on the toolbar. ![]() Before starting work on this question, type rrefmovie at the MatLAB prompt. Gaussian Elimination and Reduced Row-Echelon Form Now that you know how to do matrix calculations with MATLAB, you can easily carry out the steps in Gaussian elimination. (See Theorem 1.3 on page 24 of the text.) Question 4. Insert comments in your diary file that explain the properties of the matrix-vector product that these calculations illustrate. A u + A v, A ( u + v ), ( A + B ) u, A u + B u, A ( 3 u ), 3 A ( u ) (See Theorems 1.1 and 1.2 on pages 6 and 7 of the text.) (b) To obtain the matrix-vector product Au using MATLAB, you must type A*u (remember that a vector is just a matrix with one column). A + B, B + A, 6 B, 2 ( 3 B ), 6 A + 15 B, 3 ( 2 A + 5 B ) 3 A ′ ( 3 A T ) T Insert comments in your diary file that explain the properties of matrix addition and scalar multiplication that these calculations illustrate. The transpose A T of A is obtained by typing A ′. This is only defined when A and B are the same size. (a) To obtain a finear combination s A + tB of the matrices A and B (where s and t are real numbers) usifig MatLAB, you must type s ∗ A + t ∗ B. Matrix Addition and Matrix-Vector Multiplication Generate vectors u and v and matrices A and B by typing u = f i x ( 10 ∗ rand ( 3, 1 )), A = f i x ( 10 ∗ rand ( 2, 3 )), v = f i x ( 10 ∗ rand ( 3, 1 )), B = f i x ( 10 ∗ rand ( 2, 3 )) These matrices have entries randomly selected from the numbers 0, 1, …, 9. ![]()
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