Question

Solve the following system of homogeneous equations , 3x + 2y + 2z =0, 4X – 3y -2z=0, 5x+9y+23z=0.​

Answer 1

Answer:

(i) The matrix form of the above equations is The above matrix is in echelon form.  Here ρ(A, B) = ρ(A) < number of unknowns.  The system is consistent with infinite number of solutions.  To find the solutions.  Writing the equivalent equations.  We get  3x + 2y + 7z = 0 ……. (1)  -17y – 34z = 0 ……. (2)  Taking z = t in (2) we get -17y – 34t = 0  ⇒ -17y = 34t  ⇒ y = -2t  Taking z = t, y = -2t in (1) we get 3x + 2(-2t) + 7t = 0 ⇒ 3x – 4t + 7t = 0  ⇒ 3x = -3t  ⇒ x = -t So the solution is x = -t; y = -2t; and z = t, t ∈ R (ii)  (ii) The matrix form of the equations is (i.e) AX = B  The augmented matrix [A, B] is The above matrix is in echelon form also ρ(A, B) = ρ(A) = 3 = number of unknowns  The system is consistent with unique solution, x = y = z = 0 (i.e)  The system has trivial solution only.Read more on Sarthaks.com - https://www.sarthaks.com/864966/solve-the-following-system-of-homogeneous-equations-i-3x-2y-7z-0-4x-3y-2z-0-5x-9y-23z-0