Question

Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0 0] A) Reduced echelon form B) Neither C) Echelon form The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution. 41 -5 -1 Lo 07 B) (-1,7) C) No solution A) x1 = -1 + 5x2 x2 = 7 X3 is free D) x1 = -1 + 5x2 X2 is free 110 6 31 5) 0 1 -2 -3 10000 D) No solution A) x1 = 3 - 6x3 X2 is free x3 = 3 + x2 B) x1 = 3 - 6x3 x2 = -3 + 2x3 X3 is free C) x1 = 3 - 6x3 X2 = -3 + 2x3 x3 = 0

Answer 1

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Soli - X, + x2 + x3 = 7 Y,-*2+2x3 = 7 5x, ++x3 = 11 Augumented matrix of above system rii 171 Race R-RI Î Il! 1-1 21 Rzf Ra - SR 1 0-21 24 L 5 ! To-4-4 si 1 1 1 1 R2E-12 R2 -4 1-24 -4 1 0 R3+482 | o 1-1/2 Oo-6 RgE R3(-1/2) 3 - R2E R2 + 1 R3 Ret Ri-R3 - correspondo sysh . x2=2 - X3=4 RI E R2-R2 riool! 1 3 1 0 2 1oo1 14 Here equation of this system has a form zero = Non zero =) given system is consistent so B yes is correct