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

9127 Solutions
4164 Solvers

Last Solution submitted on Apr 18, 2021

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

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.

ZAHID RAZZAQ on 5 Nov 2020

It is tricky problem.
A=[cos(theta) sin(theta); -sin(theta) cos(theta)]; % coefficients of X1 and X2
b=[1;1] % It is a column vector

Solution Comments

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 Solvers4164

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 Solvers4164

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 Solvers4164

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players