Question

2) The row echelon form of a system of linear equations is given. a) Write the system of equations corresponding to the given matrix. Use x, y, z; or X1, X2, X3, X4 as variables. b) Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. 1 0 2 4 0 1 -1 2 1] 2 [1 2 317 i) 0 14 21 Lo o 03] il) 0 0 i 2 0 42] 10 1 1 3 3 To ooo Looooo 1 iii) 3 0 Lo 001-

Answer 1

ci ſi 2 3117 0 4 2 ou 13 osw Ax=b = 123 ) [a). Lou JJ LEJ x+2y+37 = 1 oxty +4z=2 02 Foyto 2 - 3 9(A)= P(AB) in consistent Conssistance of inconsistance if PLAIZP(AB) cji | 1 2 1 0 1 1 1 01 -12 2 ou 13 o د نا 2 - | ا د P(A) = Q(AGB) Consistence Ax= b 24o 6 | - | 2 || x, Looi3|| x2 oso 1 JL séu Con 21+ 2x2 + 4x3= 1 - X2+(-x₂) + 2xy =9 -6 Xz+ 3x4 = 0 - 3 Jxu=-2] - n =1 X3 + 38420 = X3+3(-2) = 0 ) {*3=6 | Xz - X3 + 2x4=2 =) X2-6+2(-2) = 2 A F *,+2x2 + 482=1 X2 -10 = 2 []2=127 = x,+24+24=1 21x, = -47] -47 X2 2

ſi 2 ou 2 ) * BCC Jm oo cown ا د د د ل ا د Ax=b =) 2o47 rx,7 l 2040 Jol 13 | X21. too lo Loo 0124] ссор 9(A)= PLA:5) consistent x,+2x2+0x3t 4x4=2 x2 + x3 + 38473 [x3= o tabe (X4=t Xzt X3+384 = 3 [x2= 3-3t X1 + 20627 4X4 = 2 =) X1+2(3-34) + 4 (t) = 2 = x,+ 6-6tt ut=2 = X, +6-26 = 2 => X = 2-6+2+ =1900,= 2t-4 Solution Space S t X2 tEIR o ó o to c