Suppose there are number a b c and for which a 7 1 1 3 b 1 4

Suppose there are number a, b, c and for which |a 7 1 -1 3 b 1 -4 6 0 c -5 4 -1 10 d| = 200. Find all solutions to the system ax_1 + 7x_2 + x_3 - x_4 = 0 3x_1 + bx_2 + x_3 -4x_4 = 0 6x_1 + cx_3 -5x_4 = 0 4x_1 - x_2 + 10x_3 + 2x_4 = 0

Solution

Given determinant of coefficient matrix of the system AX=0 , not equal to zero

i.e Rank of A=4= Number of unknowns in the system

Thus, the homogeneous system has unique solution

Now the unique solution of the homogeneous system is trivial solution

i.e x₁=0,   x₂=0,  x₃=0,  x₄=0,