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)