Cramer's Rule - 2x2 & 3x3 Matrices - Solving Systems of Linear Equations - 2 & 3 Variables

This algebra video shows you how to solve systems of linear equations with 2 or 3 variables using cramer's rule. This video contains plenty of examples and practice problems for you to work on.
Use Excel To Solve Systems of Equations: • How To Use The Solver ...
Introduction to Matrices:
• Intro to Matrices
Adding and Subtracting Matrices:
• Adding and Subtracting...
Scalar Multiplication of Matrices:
• Scalar Multiplication ...
Solving Matrix Equations:
• Solving Matrix Equations
Multiplying Matrices:
• Multiplying Matrices
__________________________________
Gaussian Elimination & Row Echelon Form:
• Gaussian Elimination &...
Gauss Jordan Elimination:
• Gauss Jordan Eliminati...
Gaussian Elimination With 4 Variables:
• Gaussian Elimination W...
Inverse of a 2x2 Matrix:
• Inverse of a 2x2 Matrix
Inverse of a 3x3 Matrix:
• Inverse of a 3x3 Matrix
__________________________________
Determinant of 2x2 and 3x3 Matrix:
• Determinant of 3x3 Mat...
Determinant of 4x4 Matrix:
• How To Find The Determ...
Cramer's Rule - 2x2 Linear System:
• Cramer's Rule - 2x2 Li...
Cramer's Rule - 3x3 Linear System:
• Cramer's Rule - 3x3 Li...
___________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

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[@samanthabischoff6660]

Mistake at 1:58. Should be c1b2-c2b1.

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tip. you don't have to find value of z . when you have x & y just place the values in the equation and find z in the 1 variable equation . its not that much but 2 min is 2 min

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Hi, this is the best understanding I've had so far. Thank you so much but I'm confused at 1:58 and also at 5:00.

[@tis_i_sana]

I think he made a mistake!

[@legendarysupernerd]

I also think he made a mistake. Glad to see I wasn't the only one noticing. Thought it was a change in the way the math worked and my lack of knowledge, but the next example did the determinant the normal way.

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Excellent video tutorial... Great for anyone needing to revisit the application of Cramer's Rule.

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[@olivierkalalamkofficiel6877]

the formula for dx you said is: c2xb1 - c1xb2 and in the example you use the inverse

[@shanecurrie3192]

Quick question, hope someone can help. He states that to find Dx the equation is Dx=c2b1-b2c1... but when solving for Dx he does Dx=c1b2-b1c2. This obviously equates to two totally different answers (changes the answer from 38 to -38). Which is the proper way of solving as one is said and written, but another is used?

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Taking college algebra one and reading ahead to matrices. Test is on logs and systems. I wonder if cramers rule is either neater on paper or will help me with accuracy or if it's a shorter time to solve. Anyway cheers and thanks for the clear and thorough explanation! Maybe I can impress the professor with this method on the test...

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The process is great but i would rather use basket weave for D, Dx,Dy and Dz

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[@alexandratenshi7714]

Hi. at the beginning you said for D of x - c2b1-b2c1 => then you changed the formula to usual 2x2 as c1b2-b1c2. Just fyi

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[@jayjtrainer]

why is it c2b1 - b2c1 at 2:08? I thought it should've been b2c1 - c2b1? The example at 5:15 doesn't do this

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[@ethiopiansadvibes4551]

33:40 ..............like were you watching me?????? cause i have all my problem gone cause of just one sign change ........'sigh'

[@murdoch1190]

Please specify when a mistake is realised apart from that it seems to be a good video, that Dx equation mistake left me a bit stumped for a bit thinking its my stupidity. going to continue watching from the video now.

[@hafizascape]

You have a mistake in 1:58. Please recheck.

[@djcsr]

Yeah, that had me really confused until you started doing examples and doing Dx the right way. There is nothing worse than a great tutorial video with some little mistakes.

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[@josephpanes3430]

wat if the determinant of a 3x3 matrix is zero? can i still proceed?

[@karawewa]

1:36 should be c1*b2-c2*b1

[@lilnardodavinci2521]

there is an error 2:09 Dx is not =c2b1-b2c1 it is =c1b2-c2b1 just a small mistake if you know how to take determinant out of 2x2 matrix just knowing that matrix is
Dx
c1 b1
c2 b2
would be enough for you to solve it
when he solves it with actuall numbers theres no errors there

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[@rashiddikumusah807]

Can you find the determiner of a matrix whose rows and columns are different

[@kaffuchino8244]

If the determinant D is zero, does it mean to say there is no solution for the given equations?

[@Engr-vy3in]

if Cramer works fine for 3x3 matric then why to use gaussian elimination which is a bit lengthy ?

[@gianniskallionis6687]

On 2:07 you display that Dx is c2*b1- b2*c1 whilst it is the opposite. Dx= c1*b2-c2*b1

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nice

[@leoking1653]

there is a mistake on the formula to calculate Dx (where you said : C2B1-C1B2)

[@saththiyambharathiyan8175]

why the determinant of 3 by 3 matrix is calculated in that way ? what is the intuition behind that.... I under stand 2x2 matrix determinant is obtained by elimination of variable...... But I do not understand the concept of elimination in 3x3 matrix...........

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[@elysiumx6809]

3:49 14:46