Problem 44946. Solve a System of Linear Equations

Created by Pooja Lalan

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Example</w:t></w:r><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If a system of linear equations in</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x&amp;#8321</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x&amp;#8322</w:t></w:r><w:r><w:t> is:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>2</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x₁</w:t></w:r><w:r><w:t> + </w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x₂</w:t></w:r><w:r><w:t> = 2</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>x₁</w:t></w:r><w:r><w:t> - 4 x₂ = 3</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Then the coefficient matrix (A) is:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[2  1\n1 -4]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>And the constant vector (b) is:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[2\n3]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>To solve this system, use</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>mldivide</w:t></w:r><w:r><w:t> (</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>\\</w:t></w:r><w:r><w:t> ):</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[x = A\\b]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Problem</w:t></w:r><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given a constant input angle θ (theta) in radians, create the coefficient matrix (A) and constant vector (b) to solve the given system of linear equations in</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x&amp;#8321</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>x&amp;#8322</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>cos(θ) x₁ + sin(θ) x₂ = 1</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>-sin(θ) x₁ + cos(θ) x₂ = 1</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

10061 Solutions
4626 Solvers

Last Solution submitted on Jun 20, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Vijay Anand Ramachandran on 26 Apr 2020

The problem statement clearly states to use mldivide (\)
How can the leading solution be cos(theta)+sin(theta)*[-1;1]

Sindhuja Thonti on 20 Jul 2020

My code is working perfectly on my desktop Matlab version, but here it's not accepting and displaying as incorrect..anyone help me out!

goc3 on 29 Sep 2020

The syms function is in a toolbox—Cody does not currently support any toolbox functions.

Solution Comments

Solution 5865410

3 Comments

3 Comments

ILYAS BOUALLAL on 28 May 2021 at 21:31

Your last solution is false.
I had to use a trick to get a pass.

ILYAS BOUALLAL on 28 May 2021 at 21:32

it's [0.3982; 1.357] and not [1.357;0.3982]!!

goc3 on 1 Jun 2021 at 13:06

The last test case is correct...
Your solution has the -sin() and +sin() flipped.

Solution 5851940

3 Comments

3 Comments

Nicholas Ferguson on 27 May 2021 at 16:38

Does anyone know how the 'size' value is calculated? Is it related to the # of lines of code, or the complexity? Does anyone have any tips regarding how to reduce size? I keep writing high 'size' code...

Dyuman Joshi on 27 May 2021 at 18:34

"Cody uses a node-count calculation to determine the solution size based on the number of nodes in the parse tree. Think of size as code length." - via the Official Cody homepage.

You can reduce size by reducing no. of operations as well as no. of variables.

function y = plus_one(x)
y = x+1;
end
Function size = 12

function y = plus_one(x)
z = x;
y = z+1;
end
Function size = 16

For an example related to this question, instead of defining b, you can do x = A\[1;1].
You can also take a look on other user's solutions to get some more idea.

However, in the long run that is not the best practice you would want to learn. As we write complex code, defining variables clearly and explicitly helps understand the code better. I would say what you have done is a good example of a clean code.

goc3 on 1 Jun 2021 at 12:58

That is a very helpful comment, @Dyuman Joshi.

Solution 3881673

1 Comment

1 Comment

Ryan Chapman on 27 Nov 2020

What is this? I don't even understand the question?
The answer is:
A=[cos(theta) sin(theta); -sin(theta) cos(theta)]; % coefficients of X1 and X2
b=[1;1] % It is a column vector

Solution 3866978

1 Comment

1 Comment

Dan Lecoutre on 26 Nov 2020

how tf do u do this

Solution 3001747

1 Comment

1 Comment

Siam Sadik on 28 Sep 2020

whats wrong with this problem, it runs perfectly on my matlab.
Developers guys, you should fix this problem

Solution 2943058

1 Comment

1 Comment

Ryan Chapman on 27 Nov 2020

Good job!!!

Solution 2055583

1 Comment

1 Comment

Ryan Chapman on 27 Nov 2020

lol

Problem Recent Solvers4626

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44946. Solve a System of Linear Equations

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4626

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Problem 44946. Solve a System of Linear Equations

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4626

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players