    then, 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   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.  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 #.:
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)  