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

5674 Solutions
2460 Solvers

Last Solution submitted on Oct 21, 2020

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 at 16:35

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

Solution Comments

Solution 3001747

1 Comment

1 Comment

Siam Sadik on 28 Sep 2020 at 12:27

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

Solution 2943058

1 Comment

1 Comment

Alexander Ticona on 28 Sep 2020 at 19:54

function x = solve_lin(theta)
A=[cos(theta) sin(theta); -sin(theta) cos(theta)];
b=[1; 1];
x=linsolve(A,b);
end

Problem Recent Solvers2460

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 Solvers2460

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 Solvers2460

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players