Question

show that the homogeneous system of equations 3x+2y+7z=0 , 4x-3y-2z=0 , 5x+9y+23z=0 , has no trivial solutions. also, find the solution by using matrix method​

Answer 1

rank of (A) is 2 and rank of (A, B) is 2 < 3.

3x + 2y + 7z = 0 -----(1)

-17y - 34z = 0 -----(2)

Let z = t

-17y = 34t

y = 34t/(-17) = -2t

By applying the value of z in (1), we get

3x + 2(-2t) + 7t = 0

3x - 4t + 7t = 0

3x = -3t

x = -t

Hence the solution is (-t, -2t, t)

(ii) 2x + 3y − z = 0, x − y − 2z = 0, 3x + y + 3z = 0

Solution :

Rank of A is 3 and rank of (A, B) is 3.

Since rank of A and rank of (A, B) are equal, it has trivial solution.