then,

be the quadratic polynomial

Let

5. Find a polynomial that passes through the points (-1, 6), (1, 2), (2, 3). Solve the system by computing the reduced row echelon form of the augmented matrix.

or

The system will have a unique solution, i.e., the lines will intersect at a point if

Check using Mathcad

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

intersect at a point on the plane.

Form the augmented matrix

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

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

Not possible because the maximum rank is 3 and the number of unknowns is 4.

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

a) 3 equations in 2 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:

Form the augmented matrix

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

Thus,

and

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

b) Compute the inverse of the coefficient matrix A

a) Write the system in matrix form Ax = C

2. Given the system

and

Math 002-042

Major Quiz 3

May 25, 2005

Name:

Student ID:

Section #.:09

List #.:

Answer all questions. Show all your work

1. Solve for x and y

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

==>

Thus,

Divide by 2 then factor

==>

or

Substitute in (3)

Thus, the solutions are

and

Thus,

and

3. Solve the nonlinear system

(1)

(2)

(3)

Solve for x

Substitute in (1)