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Practice problems – AMAT181 Matrices in MatLab Student’s Name: Part 1: Solving Linear Systems using Crame’r Rule a11 x a12 y a13 z b1 The system of equations a21 x a22 y a23 z b2 a x a y a z b 32 33 3 31 can be written in the form A.x b where, a11 A a21 a 31 a12 a22 a32 a13 a23 , a33 b1 x x y , b b2 . z b3 Obtain the determinants A , x , y , and z by replacing the column in A of the x, y, and z-coefficients respectively by b. Thus we have a11 a12 a13 b1 a12 a13 a11 b1 a13 a11 a12 b1 A a21 a22 a23 x b2 a22 a23 y a21 b2 a23 z a21 a22 b2 a31 a32 a33 b3 a32 a33 a31 b3 a33 a31 a32 b3 Using Cramer’s rule, the solution of the system x y x , y and z z Exercise 1: Given the following set of equations find the solution using Cramer’s rule: 2x 3y z 4 3x y 2 z 13 x 2 y 5 z 11 Step 1: Create the matrices needed to calculate the determinants , x , y , and z . Copy your work here Page 1 of 4 Practice problems – AMAT181 Step 2: Calculate the determinants , x , y , and z . Copy your work here Step 3: Use Cramer’s Rule to find the values of x, y, and z. Copy your work here Page 2 of 4 Practice problems – AMAT181 Part 2: Some more build-in functions in MatLab and Solving Linear Systems using Gaussian Elimination Exercise 2: Given the following set of equations find the solution using Gaussian Elimination 2x 3y z 4 3x y 2 z 13 x 2 y 5 z 11 Step 1: Create the matrix A and vector b . Copy your work here Step 2: To find the solution (i.e. the values of x, y and z) use x = A\b. (\ = left matrix divide, see help mldivide for details) Copy your work here Page 3 of 4 Practice problems – AMAT181 Part 3: Inverse matrix method Exercise 3: Given the following set of equations find the solution using the inverse matrix method 2x 3y z 4 3x y 2 z 13 x 2 y 5 z 11 Step 1: Create the matrix A and vector b . Copy your work here Step 2: To find the inverse matrix of A. (inv(A)) Copy your work here Step 3: Find the solution of the system (i.e find x, y, z) by multiplying A1 b Copy your work here Page 4 of 4