Question

Use Cramer’s Rule to solve the system. x − 6y = 3 3x + 2y = 1

Answer #1

we are given system of equations as

we can find determinant

now, we can find x and y

now, we can plug values

so, we get solution as

**..........Answer**

6) Cramer’s Rule
Solve each using Cramer’s rule
a) 3x + .5y =10
10x - -y =
-3
b) x + z +y = 12
-x + 3y - z = 2
-2x + z = -2
7) Proofs
Prove the following by induction
1. n3 – n is divisible by 3 for n
>=2
2. . Prove that n! <
nn forn ≥ 2.
Prove directly that:
The sum of an integer and its cube...

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

Solve the following system by Gauss elimination: x + 2y?z = 22 x
+ 5y?2z = ?17 x + 17y + 5z = ?1. Solve the system in from above by
using Cramer’s rule. First discuss the applicabililty of Cramer’s
rule to the system.

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.

Use Cramer’s Rule to solve the equations :
? − ? + 2? = −3
4 = ?3 + ?2 + ?
3− = ? + ? + ?2

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

Given the parallel planes x + 2y + 3z = 1 and 3x + 6y + 9z = 18.
Find a normal vector to these planes.

Solve the system of equations by method of the Laplace
transform:
3 dx/dt + 3x +2y = e^t
4x - 3 dy/dt +3y = 3t
x(0)= 1, y(0)= -1

Use the Inverse to solve the column vector variable matrix or
use Cramer’s Rule and solve the same column vector variable
matrix.
3x1+ 4x2 - 3x3 = 5
3x1 - 2x2+ 4x3 = 7
3x1+ 2x2 - x3 = 3

Solve x^2y’’-4xy’+6y=ln(x^2)

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