Question

2.Use separation of variables to solve (3x^2(1-y^2))/2y with initial condition y(1)=2.

3.State the solution of the homogeneous ODE with roots of its characteristic equation of r= 1,1,1,+-7i,3+-5i.

4.Consider the system of linear equations:

2x+6y+z=7

x+2y-z=-1

5x+7y-4z=9

solve this system using: a) Carmer's rule, b)Gauss-Jordan elimination, c) an inverse matrix.

Answer #1

Use Gauss-Jordan Elimination to solve the following system of
equations.
−4x
+
8y
+
4z
= −4
−3x
+
6y
+
3z
= −3
x
−
2y
−
z
= 1

3x+2y=2,6x+4y=1, 5y+z=-1 solve system of eq using gauss jordan or
gauss elimination

Solve the sytem using elimination. Do not use augmentive
matrix.
(a) 3x - 2y + z = 2
(b) 5x + y - 2z = 1
(c) 4x - 3y + 3z = 7

1) Solve by Substitution.
{x+2y=−1
{-6y=3+3x
a) One solution:
b) No solution
c) Infinite number of solutions
2) Solve by Substitution
{4x+y=−15
{2y=-27-8x
a) One solution:
b) No solution
c) Infinite number of solutions
3) Solve the system by elimination.
{−x−2y=4
{2x+2y=-8
a) One solution:
b) No solution
c) Infinite number of solutions

4. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions. In the latter case, present
the solutions in parametric form.
3x + 6y + 3z = -6
-2x -3y -z = 1
x +2y + z = -2

Solve the system using 3x3
3x-2y+z=2
5x+y-2z=1
4x-3y+3z=7

Use Gauss-Jordan Elimination to solve the following system of
equations.
2x
−
2y
= 1
6x
−
8y
= −2

1) Solve these equations: 3x-y=-11
x+2y=8
2) Solve these equations:
x+y+z=6
x-y-z=-4
2x+y-4z=-8

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

Sec 6.2
1.Write an augmented matrix for the following system of
equations.
9x-8y+6z=-1
7x-5y+2z=9
6y-8z=-9
The entries in the matrix are ?
2.use row operations on the augmented matrix as far as necessary
to to determine whether they system is independent, dependent, or
inconsistent ?
4x-6y+5x=-2
-8x+12y-10z=4
-12x+18y-15z=6
3. use row operations on the augmented matrix as far as
necessary to to determine whether they system is independent,
dependent, or inconsistent ?
5x-7y+4z=13
-5x+7y-4z=-15
-10x+14y-8z=-27
4. Solve the system by...

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