Cramer's Rule Explained

Determinant of a 2x2 Matrix: • How to find the Determ...
Determinant of a 3x3 Matrix: • Determinant of a 3x3 M...
Cramers Rule
Cramer's rule is invented by mathematician Gabriel Cramer in 1750s. This rule is used to find the solution of a system of equations with any number of variables and the same number of equations. Sometimes, when we are solving a system of equations in 3 variables, say x, y, and z, we may need to solve for two variables x and y to solve for variable z. But using Cramer's rule, we can find the value of any variable without finding the values of the other variables.
But this rule has some limitations with respect to the solutions. This rule can be applied only when the system has unique solutions. But how do we know when a system has unique solution? Let us learn more about this along with the definition and formula of Cramer's Rule.
What is Cramer's Rule?
Cramer's rule is one of the methods used to solve a system of equations. This rule involves determinants. i.e., the values of the variables in the system are found with the help of determinants. Let us consider a system of equations in n variables x₁, x₂, x₃, ..., xₙ written in the matrix form AX = B, where
A = the coefficient matrix which is a square matrix
X = the column matrix with variables
B = the column matrix with the constants (which are on the right side of the equations)

[@iqinitiative]

How to find:
• The determinant of a 2x2 Matrix: ua-cam.com/video/L9QZODoMWlQ/v-deo.html
• The determinant of a 3x3 Matrix: ua-cam.com/video/jPYt76Jsw34/v-deo.html

[@meshackjaramba]

value for y should be 3

[@PethrishaSteven-oi9ur]

How did you get 5 when you subtract 6 from 21 for the y?

[@ChipangoMuti-c2n]

I wondered as well 😂

[@iqinitiative]

Mistake

[@muhammadt.squire7274]

Uu really knows how to teach.God bless you ❤.

[@iqinitiative]

I'm grateful 🙏😌

[@lexinamweemba4690]

Sir for y it's 15 not 5 when we subtract 21-6=15

[@iqinitiative]

Yes. I've seen it. Thank you for the correction.

[@johnymnemonic4657]

Exactly 21-6=15

[@ApiaryManager]

The explanation is good but there are a few arithmetic mistakes (as others have said). Therefore, I suggest people just follow the method and not pay too much attention to the arithmetic errors.

[@iqinitiative]

👍

[@CarolineMuzirwa]

Guys who else realized that we are supposed to divide with -62as D not 62 so our solution sets should be positive

[@naomabuga-c1n]

Thanks sir you make me to understand more may God add you more days

[@iqinitiative]

You are welcome and thank you so much

[@JoramShimishi]

21-6=15......on y determinant

[@p.prajwalla]

Actually........
When I realised I been started searching for this kinda comment

[@Kenya2030]

Thanks alot sir really understood the concept

[@iqinitiative]

You are most welcome

[@girldev1013]

Sir I think the value of why I is suppose to be 3, because 21-6 is 15 not 5

[@vibewithpeter9424]

does the formula work for a 3x3 matrix

[@fredricksakawa3886]

Great stuff

[@iqinitiative]

Glad it was helpful 😊

[@ObertChileshe-me2jl]

Sir the determinant is negative 62 and not positive,all those answers are positives.i submit.

[@tresphordkabwe1979]

Sir in the first equations the value of Dy is suppose to be ( 21- 6 =15) and not 5

[@iqinitiative]

Yes noted. Kindly correct it.

[@MariaErastus-tl2ik]

But 21-6 =15 ...where did you get the 5 from

[@iqinitiative]

Mistake

[@mr.stranger3417]

Thank you 😊

[@ObertChileshe-me2jl]

Good work, just minimise your mistakes

[@iqinitiative]

Sure. Thanks.

[@nurudeenabdulganiyu3837]

I want to commend you for a good job. But please work on the audio, the audio is not audible enough. Thanks

[@iqinitiative]

Yes I agree. Working on that. Thank you👍

[@lesedisehularo-wf2ou]

D is -62 plz don't forget negative on ur final answers

[@Festuspetrus-mz6jy]

Why did you put a positive 2

[@aheia_kevin]

Value of y is =15

[@iqinitiative]

Yes

[@EricwasenHaau]

The value of Dy should be 15. From 21-6

[@iqinitiative]

👍

[@anniemangoche587]

Thank u

[@iqinitiative]

You're welcome

[@calvinharrison7680]

Ans is × =1,y=3

[@wandishabanda8433]

On DY I think 21minus six can not give 5, it is suppose to be 16

[@iqinitiative]

Yes

[@salami19-v4t]

good video thanks

[@iqinitiative]

Glad you enjoyed it

[@OscarKanyimbo]

Sir on the last question I think the value of x is 8 not 7

[@iqinitiative]

Check properly my friend. Try to prove your answers too.

[@OscarKanyimbo]

I have done that about three times so but still it is giving me 8

[@angelawainaina-uz8tr]

25:44 Yes please...the value of x is -8 not -7. Thanks

[@gracebanda-l1l]

How may I solve for single logarithm

[@iqinitiative]

To solve a single equation or simultaneous equations?

[@randomcomputer7248]

great video !

[@iqinitiative]

Glad you enjoyed it

[@offiongessien7217]

How was -62 got please

[@johnaismael729]

The first example Dy=15 and not 5

[@iqinitiative]

Yes. It was just a mistake.

[@iqinitiative]

Thanks

[@DophtonPeter]

21-6 is not =5.Its 15.

[@MusondaJustina]

Value of y is 3

[@iqinitiative]

Yes

[@AyeyiChyerl]

Please the Dy is 15 not 5

[@iqinitiative]

You are welcome and all the best

[@bhimasenmuddapur]

Dy =15 not 5

[@iqinitiative]

Yes

[@SibajeneMatende]

Great

[@iqinitiative]

cool

[@danielnegussie4894]

You made a mistake 21 minus 6 is not 5

[@iqinitiative]

Yes, thank you for the correction.

[@anasmikail9276]

I don't know if I should believe myself or not but I think 21 - 6 is 15 😅

[@iqinitiative]

Yes. It was an error when making the video.

[@iqinitiative]

3x3 ROW OPERATION: 👇👇👇
ua-cam.com/video/qjsd7N9MKJ4/v-deo.html

[@Eneswar]

watched some of your videos and you are making a lot of mistakes...

[@nkosinathimbongiseni9059]

Like he said 21-6=5😢

[@KennieMwas]

excuse me sir DY=15

[@iqinitiative]

Yes. It was a small error

[@Kenya2030]

Lets everyone who get concept from this lecture to subscribe to pay him back for his good job

[@iqinitiative]

🙏