augmented matrix, Gaussian elimination

augmented matrix, Gaussian elimination 150 150 Affordable Capstone Projects Written from Scratch

Please show all working and justify your answers.

  1. (8 marks) Consider the system of equations with constants a and b:

−x + 3y + 3z = 6

x + 2y − 4z = 6

−2x + y + az = b.

(a) Write the associated augmented matrix for this system of equations.

(b) Use Gaussian elimination to reduce the matrix to row echelon form. (Do not go all the way to

reduced row echelon form.)

(c) For what values of a and b does the system have

  1. no solution,
  2. infinitely many solutions,

iii. a unique solution?

(d) Solve the system of equations for the case a = 0 and b = 7.

  1. (4 marks) Consider the line L in R3, given by x = −

 

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