Question

r+2y [9] 1. Consider the system of equations: = 5 6y - 32 = -1 + 2z = 0 4.2 a) Rewrite the system as a matrix equation AX = B, being sure to clearly label A, X, and B. b) Calculate the matrix adj(A). c) Calculate det(A). Show your work!

Answer 1

Given; Equation is: system of linear xtay 51 by-3z = -1 4.91 +2Z = 0 AX =B Solution a) where 2 x b G-3 x=y B= -1 1 2 Z 2 2 G -3 4 4. 2 2. O NA Adj(A):- o factor elements of A is 20 An - - 6x2+3x0 A1 =- 2262-020 2 An = 12 Az - 4 AR = 16.2 tail 121 -( 0x2 +3xa) A22 = - 172-004 4 2 A12 = -12 A22 = 2 maal 21 0 A23 - 2-(6-8) AB = - oxo- 6x4 4018 4. 4 0 A1 = -2.4 A23= 8

2 A31 1 -243-0 133 6 A31 - - - 16-20 - 6 A32=- 1- -61X3-02 A-33 = 6 432 = 3 T + 412 A13 12 Adj(A)= -12 24 21 12 A22 A23 2 M31 A32 433 -G 12 - 4 -67 . Adj(A) = -12 2 الما 2.4 8 6 2 0 c) del A 0 6 4 0 2 G - 3 -3 TAL - 2 -7.6 IAL 21 (6x2-0) -2 (0+12) to = 12 - 24 - 12 ..^= -12

I adj (4) IAL 12 CY - -IZ -12 8 G 2.4- 12 12 2 3 1 2.4 8 G AX =B X = AB 12 -4 - S 1 12 2 2 3 24 8 D 12x5 +4x16x0 6044 64 12 1-12XS-2X1 +380 1 12 |-60-2 = -62 2445–8X14670 12-8 112 5-64/12 . 112/12 3% - 28/2 16 Hence, Solution is. De y = 31 Z -28 3