Cramer's Rule Explained

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)

[muhammadt.squire]

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

[PethrishaSteven-oiur]

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

[naomabuga-cn]

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

[lexinamweemba]

Sir for y it's 15 not 5 when we subtract 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.

[CarolineMuzirwa]

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

[Kenya]

Thanks alot sir really understood the concept

[vibewithpeter]

does the formula work for a 3x3 matrix

[tresphordkabwe]

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

[girldev]

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

[MariaErastus-tlik]

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

[wandishabanda]

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

[nurudeenabdulganiyu]

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

[EricwasenHaau]

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

[OscarKanyimbo]

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

[ObertChileshe-mejl]

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

[ObertChileshe-mejl]

Good work, just minimise your mistakes

[lesedisehularo-wfou]

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

[danielnegussie]

You made a mistake 21 minus 6 is not 5