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)
