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...
___________________________________
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www.video-tutor.net/
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[@TheOrganicChemistryTutor]

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Determinants is not a part of calculus

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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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@@tis_i_sana Guess you are a mistake

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[@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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[@olivierkalalamkofficiel6877]

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

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[@josephpanes3430]

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

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[@kellymoore5517]

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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[@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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[@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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[@kaffuchino8244]

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

[@rashiddikumusah807]

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

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[@Engr-vy3in]

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

[@edb452]

is the middle one at 17:00 always negative?

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At 17:00 can someone explain why the middle one is negative?

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[@mathmentorvideotutorial5703]

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

[@a.mp.m7340]

In the beginning of the video with 13(-5) - (3)(-9) how did you get positive 27 shouldn't it be negative 27 because of the -9? You said -3×-9 Im trying to see how that is. The last problem was left a positive but this one was changed to a negative, why?

[@djcsr]

He just skipped a step there. It is negative 27 but then you subtract negative 27 which is the same as adding positive 27.

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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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[@jesseludenyo6436]

where is the negative middle sign coming from?

[@karawewa]

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

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[@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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3:49 14:46

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[@leoking1653]

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