How Do You Solve a System with Variables and Constants?

[JaZZyCooL]

Homework Statement

Solve the following system of equations

Homework Equations

A1 + A3 = 0
cA1 + A2 + A4 = 0
dA1 + cA2 + w^2 A3 = 1
dA2 + w^2A4 = 0

The Attempt at a Solution

https://imgur.com/YSG5oGN - Page 1
https://imgur.com/dGbccsE - Page 2

 

[kuruman]

I checked with Mathematica. Your expressions for A2 and A4 are correct. Your expression for A3 is not.

 

[scottdave]

I checked with Mathematica. Your expressions for A2 and A4 are correct. Your expression for A3 is not.

Knowing that, the OP should be able to easily fix A1 and A3.

 

[kuruman]

Knowing that, the OP should be able to easily fix A1 and A3.

I agree. This particular system lends itself to using Cramer's rule because of all the zeroes on the right hand side.

 

[SammyS]

Homework Statement

Solve the following system of equations

Homework Equations

A1 + A3 = 0
cA1 + A2 + A4 = 0
dA1 + cA2 + w^2 A3 = 1
dA2 + w^2A4 = 0

The Attempt at a Solution

https://imgur.com/YSG5oGN - Page 1
https://imgur.com/dGbccsE - Page 2

Here is your Page 1:

Here is your Page 2:

 

[symbolipoint]

the system shows two nonlinear equations. Not linear system.

 

[SammyS]

the system shows two nonlinear equations. Not linear system.

The system is linear in A₁, A₂, A₃, and A₄ .

 

[symbolipoint]

The system is linear in A₁, A₂, A₃, and A₄ .

These two equations are shown in the system:

dA1 + cA2 + w^2 A3 = 1
dA2 + w^2A4 = 0

Not linear. That shows an exponent of 2 on the w. If I misunderstand, then w is not a variable; but A1, A2, and A3 must be the variables. If this latter is the case, then yes; linear system.