AUGMENTED MATRIX TRIAL

4 Obtain the relative error (in the solution vector x r) e k = ∥ x c – x r∥/∥ x c∥. 3 Compute error-free the solution x r of the linear system represented by D r. 2 Generate m × (n + 1) uniformly distributed random (pseudo-random) numbers in the interval. 1 Compute error-free the solution x c of the system represented by D. Let the error introduced in each element of D be 0.05% and D′ be the m × (n + 1) matrix whose each element d ′ i j is an ordered pair, The evolutionary procedure is as follows. Sen, in Mathematics in Science and Engineering, 2005 6.2.1 Evolutionary approach for error estimate in exact computationĬonsider the m × (n + 1 ) augmented matrix D = of the system A x = b.

AUGMENTED MATRIX TRIAL

A trial solution x (0) is proposed and then progressively better estimates x (1), x (2), x (3), … for the solution are obtained iteratively from the formula Is F an elementary matrix? How would one construct elementary matrices corresponding to operation (E3)? 48.Ī solution procedure uniquely suited to matrix equations of the form x = Ax + d is iteration. Compute the product FA for any 4 × 4 matrix A of your choosing. Is G an elementary matrix? How would one construct elementary matrices corresponding to operation (E2)? 47.įorm a matrix F from the 4 × 4 identity matrix I by adding to one row of I five times another row of I. Is H an elementary matrix? How would one construct elementary matrices corresponding to operation (E1)? 46.įorm a matrix G from the 4 × 4 identity matrix I by multiplying any one row of I by the number 5 and then compute the product GA for any 4 × 4 matrix A of your choosing. Form a matrix H from the 4 × 4 identity matrix I by interchanging any two rows of I, and then compute the product HA for any 4 × 4 matrix A of your choosing.

45.Īn elementary matrix is a square matrix E having the property that the product EA is the result of applying a single elementary row operation on the matrix A. 44.ĭetermine the production quotas for each sector of the economy described in Problem 22 of Section 2.1.

43.ĭetermine the total sales revenue for each country of the Leontief closed model described in Problem 20 of Section 2.1. 42.ĭetermine the wages of each person in the Leontief closed model described in Problem 19 of Section 2.1. 41.ĭetermine the annual incomes of each sector of the Leontief closed model described in Problem 18 of Section 2.1. 40.ĭetermine the number of barrels of gasoline that the producer described in Problem 17 of Section 2.1 must manufacture to break even. 39.ĭetermine the bonus for the company described in Problem 16 of Section 2.1. 38.ĭetermine feed blends that satisfy the nutritional requirements of the pet store described in Problem 15 of Section 2.1. 37.ĭetermine a production schedule that satisfies the requirements of the manufacturer described in Problem 14 of Section 2.1. 36.ĭetermine a production schedule that satisfies the requirements of the manufacturer described in Problem 13 of Section 2.1. 35.ĭetermine a production schedule that satisfies the requirements of the manufacturer described in Problem 12 of Section 2.1. Use Gaussian elimination to solve Problem 5 of Section 2.2. Use Gaussian elimination to solve Problem 4 of Section 2.2. Use Gaussian elimination to solve Problem 3 of Section 2.2.

Use Gaussian elimination to solve Problem 2 of Section 2.2. Use Gaussian elimination to solve Problem 1 of Section 2.2. In Problems 18 through 24, use elementary row operations to transform the given matrices into row-reduced form: 18. Solve the system of equations defined in Problem 11. Solve the system of equations defined in Problem 10. Solve the system of equations defined in Problem 9. Solve the system of equations defined in Problem 8. Solve the system of equations defined in Problem 7. Solve the system of equations defined in Problem 6. In Problems 1 through 5, construct augmented matrices for the given systems of equations: 1.

Augmented matrix