Form the augmented matrix

then,

be the quadratic polynomial

Let

5. Find a polynomial that passes through the points (-2, -3), (0, -1), (3, 17). Solve the system by computing the reduced row echelon form of the augmented matrix.

SEE SOLUITON FOR SECTION 9

do not intersect at a point on the plane.

4. Find the values of k for which the three straight lines

Check using Mathcad

and

Thus, the solutions are

d) 3 equations in 3 unknowns that has a unique solution

c) 4 equations in 3 unknowns that has infinite number of solutions

b) 4 equations in 3 unknowns that has a unique solution

a) 2 equations in 3 unknowns that has no solution

6. Extra Credit: If possible, give examples of the reduced row echelon form of the augmented matrix of a linear system with the given property. If not possible, write "Not Possible" as an answer. Use " * " to indicate that an element could be any real number.

Check using Mathcad

The polynomial is:

and

Thus,

This is the reduced row echelon form of the augmented matrix.

b) Compute the inverse of the coefficient matrix A

a) Write the system in matrix form Ax = C

2. Given the system

and

Thus,

==>

Equate the real and imaginary parts of the two sides of the equation

1. Solve for x and y

Answer all questions. Show all your work

List #.:

Section #.:17

Student ID:

Name:

May 25, 2005

Major Quiz 3

Math 002-042

Substitute in (3)

or

==>

Substitute in (1)

Solve for x

(3)

(2)

(1)

3. Solve the nonlinear system

and

Thus,

c) Use the inverse of A to find the solution of the system