Question

(6) Use Matrices to find the solution set of xty-22=3 34-y +z = 5 3x + 34-6=9

Answer 1

Solution: - (vorssable matsix) B=1 non homogenious system Inend egeations in the loom of Ax=B (a)man [coefficient mature and x. Consider a US let 24 whese (constant column]. B3 If Jank of A Dank of A B =n then Augranted matux No. of Variables the system contains unique Solution. are Given ean's xty- 2z =3 32-y + z = 5 3x + 3ybz = 15 these no. of varsibles n= 3 [ie, 3, 5, 15] Augmented mateix: 1 - 2 1 3 3 -1 1 5 15 . To find the Tank of augmenten makix; let us Convert it into Echolan from by using operations R₂ : 30,- R2; R₂:3R - Rz

Rq: 3R, R₂ - 2 3 4 -7 4 3 3 15 R3: 3R - R₃ - 2 3 4. -7 4. more Rank of Augrated matione = 3 which is equal to n. - it has unique solution -6Z = -6 Z=1 44-7Z=4 - 44 7(1)=4 y. axy-2Z =3 = x + 1/4 -2(1)=3 = 4