# [NEED HELP ] Linear Systems Calculations

• ivanyo
In summary, the person is seeking help with their exam preparation and is struggling with some questions related to converting between Cartesian and polar form, calculating eigenvalues and eigenvectors, and expanding complex numbers. They are especially looking for assistance with the second and third images, which they are not very familiar with.
ivanyo
Hi guys/gals,

First post here - in need of some desperate last minute help. Today is my last day to study and I will have my final exam tommorow. I've been doing past papers all day, and there a few questions I have no idea/never seen before in my course material.

Part (c) I have no idea what to do. I know I need to convert the 4sqrt2 into Cartesian, but I have no idea how...

Part (d) I'm very close to getting, but I end up getting -cos^2(theta) + (-1) sin^2(theta) = 0

Part (e) is related to part (d), so I'm not too sure at the moment.

I know that there is the rule that when there is a matrix A, A1v1=A2v2. However, these eigenvalues are imaginary, so how do I calculate the eigenvectors?

In a)i) of this question, I calculated -1/2 and -1 as the values of M (i.e. when you let Un=kM^n). I just want to double check these are correct, and also would like somebody to guide me in part ii). I have no idea how to calculate this using the results of part i)MANY MANY MANY thanks to whoever is able to help me out here. I think I may have already failed 1 subject this semster, and do not want to make it 2.

Cheers,

EDIT- extremely sorry for the image size, I don't know how to re-frame it. it's a photo from my phone haha

For the resizing thing, if you upload to imageshack there is an option for it.

First image:

c)the 4√2 is just a constant, so when you put eiπ/4 into cartesian form, you would multiply it by 4√2.

d) If you consider z1z2 in polar form you will get r2 right? So just expand z1z2 in cartesian form and then put that equal to r2 [z1 is the z in the question and z2 is its conjugate]

e) Well you want to find sin5θ, so consider expanding (cosθ+isinθ)5 (which is equak to cos5θ+isin5θ by De Moivre's theorem) and equate real and imaginary parts.

I am not too well versed on the topics in the second and third images, so I can't really help you there.

Last edited:
Thanks for the response. I think I get it a little better now.

Any takers for 2nd+3rd image?

## What is a linear system?

A linear system is a set of two or more equations with multiple variables that can be solved simultaneously to find the values of each variable.

## How do I solve a linear system?

To solve a linear system, you can use a variety of methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to eliminate or isolate variables until you are left with the solution.

## What is the importance of solving linear systems?

Linear systems are used to model real-life situations in fields such as physics, engineering, and economics. By solving these systems, we can find the relationships between different variables and make predictions or solve problems.

## What are the common mistakes when solving linear systems?

Some common mistakes when solving linear systems include not properly distributing negative signs, making computational errors, or not checking the final solution to see if it satisfies all equations in the system.

## Can linear systems have more than two variables?

Yes, linear systems can have any number of variables. However, the number of equations must be equal to the number of variables in order to have a unique solution. If there are more equations than variables, the system is considered overdetermined and may not have a solution.

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