6. a) Given that the det(H)=0, where: H= b) Given that ( 2 AT3 [ 1 2 1 1 [1 x x x 1 x x x 1 ])T = [ 2 3 1 2 ] , find the value of x ] , determine the matrix A c) A truss system with three unknown forces F1, F2, F3 is modeled using the following equations: 2F1 + 3F2 - F3 = 10 4F1 + F2 + 2F3 = 15 -2F1 + 5F2 + 7F3 = 5 Solve for F1, F2, and F3 using Gaussian elimination. d) In an electrical circuit, the node voltage equations are given as: 3V1 - 2V2 + V3 = 10 2V1 + 4V2 - 3V3 = 5 V1 - 3V2 + 2V3 = -2 Solve for V1, V2, V3 using Gaussian elimination