Solve with cramer's rule x+2y+3z=11, 2x+y+2z=10, 3x+2y+z=9

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B  

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A =  = 1(1-4) - 2(2-6) + 3(4 - 3)

                    = 1(-3) - 2(-4) + 3(1)

                    = -3+8+3 = 8

also D

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx =     = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x =  = = 2

similarly

Dy = = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = = 0

Dz= = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = =

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

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