Quiz 1:

0). For a function:

b) Use the linearization in (a) to write down the system of linear equations that are the linear approximation to the (non-linear system of) equation(s):

a) Write the associated augmented matrix;

b) Write the associated vector equation;

c) Write the associated matrix equation.

2) Write the matrix that is the next step in Gauss-Jordan elimination process, indicating which row operations you used, and whether the result is in reduced row echelon form: 

3) The following represent the reduced form of the augmented matrix [v1...vm |v ] :

a) Write out the vector equation associated to [v1...vm |v ] ;

b) Write out the system of equations associated to the reduced augmented matrix;

c) Write the set of solutions in vector parametric form or state there are no solutions: 

Quiz 2:

For a collection of vectors v1,...,vm, the reduction of [v1...vm |y ]  is displayed below:

a) Write the Consistency Condition of the system [v1...vm |y ] in vector parametric form OR state that all augmentations lead to consistent systems;

b) For an augmentation y that satisfies the Consistency Condition of [v1...vm |y ] write the solution set of [v1...vm |y ] :