Question

Consider the linear system in three equations and three unknowns: 1) x + 2y + 3z = 6, 2) 2x − 5y − z = 5, 3) −x + 3y + z = −2 .

(a) First, identify the matrix A and the vectors x and vector b such that A vector x = vector b.

(b) Write this system of equations as an augmented matrix system.

(c) Row reduce this augmented matrix system to show that there is exactly one solution to this system of equations.

(d) Convert your reduced augmented matrix system back into an equivalent system of equations, and then use back-substitution to compute the unique solution to the original system of equations.

(e) Verify that the solution vector x that you found in (d) is indeed a solution of the system of equations by computing A vector x and showing this is equal to the vector b.

Answer 1

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