Question

Solve by rank method x + 2y – 3z = -4; 2x + 3y + 2z = 2; 3x – 3y – 4z = 11

Answer 1

x + 2y – 3z = -4; 2x + 3y + 2z = 2; 3x – 3y – 4z = 11

The matrix equation is

The last equivalent matrix is in echelon form. 

ρ(A) = ρ([A, B]) = 3 = Number of unknowns 

The new matrix equation is given by

x + 2y – 3z = -4 ……. (1)

-y + 8z = 10 …….. (2) 

-67z = -67 ……… (3) 

(3) ⇒ z = 1 

(2) ⇒ -y + 8 = 10 ⇒ -y = 2 ⇒ y = -2 

(1) ⇒ x = -4 -2(-2) + 3(1) ⇒ x = 3 

Hence the solution is (x, y, z) = (3, -2, 1)