# ALGEBRA ASSIGNMENT

3

1. Solve the matrix equation for the unknown matrix X, or explain why no solution exists.  2. The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. 3)

3. Perform the matrix operation, or if it is impossible, explain why. 4. Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. 5. Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. 6. The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. 7. Solve the system of linear equations. 8. Solve for x and y. x = __________, y = ___________

9. A specialty-car manufacturer has plants in Auburn, Biloxi, and Chattanooga. Three models are produced, with daily production given in the following matrix.

Cars produced each day  Model K Model RModel W Auburn Biloxi Chattanooga

Because of a wage increase, February profits are less than January profits. The profit per car is tabulated by model in the following matrix.

January                               February

Model K Model R Model W (a) Calculate AB. AB = __________ (b) Assuming all cars produced were sold, what was the daily profit in January from the Biloxi plant? (c) What was the total daily profit (from all three plants) in February?

1 Point

10.The matrices B and C are defined as follows. Carry out the indicated algebraic operation, or explain why it cannot be performed.

6B + 3C

11. A matrix is given. (a) Determine whether the matrix is in row-echelon form.

(b) Determine whether the matrix is in reduced row-echelon form.

(c) Write the system of equations for which the given matrix is the augmented matrix. 12. Write the system of equations as a matrix equation. 13. Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. 14. Solve the system of linear equations. 15. Solve the system of linear equations.

16.The matrices A, B and E are defined as follows. Carry out the indicated algebraic operation, or explain why it cannot be performed.

ABE

17. Solve the system of linear equations. 18. The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. 19. The matrix A is defined as follows. Carry out the indicated algebraic operation, or explain why it cannot be performed.

​​A3

20. The matrices B and F are defined as follows. Carry out the indicated algebraic operation, or explain why it cannot be performed.

BF

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