Question

2) 3w - x + 12y + 18z = -4 w-2x + 4y + 112 = -13 w + x + 4y + 2z = 8 Denklem sisteminin çözümünü bulunuz.
ıt means solve the equation system

Answer 1

Salno Consider the 3 u unknouens fellowsing linear system of 3 equations in x + lay + 182 = -4 3 wkt W-out wtht hy +112 = -13 ta2 = 8 matrix is The associated augmented 18 4 1 4 8 le to this matrix to bring first reduced given need to row - echelon form matrix is 18 1 4 - 3 1 4 АН R, HR es 4 11 3 12 18 -4 Apply Rg → Ro-RI 1 - 4 O w -1 18 -4

Apply Ra 8 o 9 / -3 18 -4 Apply R We 1 1/3 4 61-4/3 Apply Rj R-RI ५ 8 7 6 -42 6 Appely R - Rz t 1 8 o o 0 o 0 The obtained reduced roul - echelon form is 18] O 0 that the system We see y? basic is consistent, and are free variables variables. el, u are

sank The •The of the sank of the also augmented matrix is a. coefficient matrix is left to express the basic variables free ones are We im terms Ly 2 = we have flowe, the of free } - free two equations, (aw th tlak, + 18 kg .-4) x2 bl-au tuk, tilkg = -13 Gul -ah tauk, +36kg = -8 w dn + 4k, + 11 kg = 713 کیا گ + dok, tarko -5 fence, W = this value in first oq of the 1-4k - ska Now, but given system, 3(1-4k, -5kg) tlak, +18 kg + 4 = 4 3-lak, -15kg tløk, +18 kg ty 3 kg +7 7 1-4kg-skg 3kg +7 k K If Mence, W = h ar 2 kg