1. Write the solution set of the given homogeneous system inparametric form. x 1

Question

1. Write the solution set of the given homogeneous system inparametric form. x1 -3x2 + x3= 0 -2x1 + x2 -x3 =0 -3x1 - x2 - x3 = 0 2. Write the solution set of the following system inparametric vector. x1 -3x2 + x3= 3 -2x1 + x2 -x3 = 4 -3x1 - x2 - x3 = 11 1. Write the solution set of the given homogeneous system inparametric form. x1 -3x2 + x3= 0 -2x1 + x2 -x3 =0 -3x1 - x2 - x3 = 0 2. Write the solution set of the following system inparametric vector. x1 -3x2 + x3= 3 -2x1 + x2 -x3 = 4 -3x1 - x2 - x3 = 11 x1 -3x2 + x3= 3 -2x1 + x2 -x3 = 4 -3x1 - x2 - x3 = 11

Explanation / Answer

1. Write the solution set of the given homogeneous system inparametric form. x1 -3x2 + x3= 0 -2x1 + x2 -x3 =0 -3x1 - x2 - x3 = 0 2. Write the solution set of the following system inparametric vector. x1 -3x2 + x3= 3 -2x1 + x2 -x3 = 4 -3x1 - x2 - x3 = 11
A= 1 -3 1 0 3 -2 1 -1 0 4 -3 -1 -1 0 11 NR2=R2+2R1…NR3=R3+3R1 1 -3 1 0 3 0 -5 1 0 10 0 -10 2 0 20 NR1=R1-3R2/5…NR2=-R2/5….NR3=R3-2R2 1 0 0.4 0 -3 0 1 -0.2 0 -2 0 0 0 0 0 WE FIND III ROW IS ALL ZERO SO DEPENDENT EQN.& CONSISTENT. SO 2 INDEPENDENT EQNS. IN 3VARIABLES SO ONE FREE VARIABLE LET Z BE THE FREE VARIABLE WE GET FROM THE LAST REDUCEDMATRIX X+0.4Z=0….X=-0.4Z Y-0.2Z=0…..Y=0.2Z SO GENERAL SOLUTION SET IS X=-0.4T…..Y=0.2T…..Z=TIS ANY REAL NUMBER . THIS IS THE GENERAL SOLUTION SET INPARAMETRIC FORM FOR THE SET OF HOMOGENEOUS EQNS WITH TAS PARAMETER.. ================================================ FOR THE NON HOMOGENEOUS EQN. WEGET X+0.4Z=-3…….X=-3-0.4Z Y-0.2Z=-2………Y=-2+0.2Z SO GENERAL SOLUTION SET IS X=-3-0.4T…..Y=-2+0.2T…..Z=TIS ANY REAL NUMBER . THIS IS THE GENERAL SOLUTION SET INPARAMETRIC FORM FOR THE SET OF HOMOGENEOUS EQNS WITH TAS PARAMETER.. THE PARAMETRIC VECTOR IS [-3 , -2 , 0 ] + T [ -0.4 , 0.2 ,1]
x1 -3x2 + x3= 3 -2x1 + x2 -x3 = 4 -3x1 - x2 - x3 = 11
A= 1 -3 1 0 3 -2 1 -1 0 4 -3 -1 -1 0 11 NR2=R2+2R1…NR3=R3+3R1 1 -3 1 0 3 0 -5 1 0 10 0 -10 2 0 20 NR1=R1-3R2/5…NR2=-R2/5….NR3=R3-2R2 1 0 0.4 0 -3 0 1 -0.2 0 -2 0 0 0 0 0 WE FIND III ROW IS ALL ZERO SO DEPENDENT EQN.& CONSISTENT. SO 2 INDEPENDENT EQNS. IN 3VARIABLES SO ONE FREE VARIABLE LET Z BE THE FREE VARIABLE WE GET FROM THE LAST REDUCEDMATRIX X+0.4Z=0….X=-0.4Z Y-0.2Z=0…..Y=0.2Z SO GENERAL SOLUTION SET IS X=-0.4T…..Y=0.2T…..Z=TIS ANY REAL NUMBER . THIS IS THE GENERAL SOLUTION SET INPARAMETRIC FORM FOR THE SET OF HOMOGENEOUS EQNS WITH TAS PARAMETER.. ================================================ FOR THE NON HOMOGENEOUS EQN. WEGET X+0.4Z=-3…….X=-3-0.4Z Y-0.2Z=-2………Y=-2+0.2Z SO GENERAL SOLUTION SET IS X=-3-0.4T…..Y=-2+0.2T…..Z=TIS ANY REAL NUMBER . THIS IS THE GENERAL SOLUTION SET INPARAMETRIC FORM FOR THE SET OF HOMOGENEOUS EQNS WITH TAS PARAMETER.. THE PARAMETRIC VECTOR IS [-3 , -2 , 0 ] + T [ -0.4 , 0.2 ,1]
A= 1 -3 1 0 3 -2 1 -1 0 4 -3 -1 -1 0 11 NR2=R2+2R1…NR3=R3+3R1 1 -3 1 0 3 0 -5 1 0 10 0 -10 2 0 20 NR1=R1-3R2/5…NR2=-R2/5….NR3=R3-2R2 1 0 0.4 0 -3 0 1 -0.2 0 -2 0 0 0 0 0 WE FIND III ROW IS ALL ZERO SO DEPENDENT EQN.& CONSISTENT. SO 2 INDEPENDENT EQNS. IN 3VARIABLES SO ONE FREE VARIABLE LET Z BE THE FREE VARIABLE WE GET FROM THE LAST REDUCEDMATRIX X+0.4Z=0….X=-0.4Z Y-0.2Z=0…..Y=0.2Z SO GENERAL SOLUTION SET IS X=-0.4T…..Y=0.2T…..Z=TIS ANY REAL NUMBER . THIS IS THE GENERAL SOLUTION SET INPARAMETRIC FORM FOR THE SET OF HOMOGENEOUS EQNS WITH TAS PARAMETER.. ================================================ FOR THE NON HOMOGENEOUS EQN. WEGET X+0.4Z=-3…….X=-3-0.4Z Y-0.2Z=-2………Y=-2+0.2Z SO GENERAL SOLUTION SET IS X=-3-0.4T…..Y=-2+0.2T…..Z=TIS ANY REAL NUMBER . THIS IS THE GENERAL SOLUTION SET INPARAMETRIC FORM FOR THE SET OF HOMOGENEOUS EQNS WITH TAS PARAMETER.. THE PARAMETRIC VECTOR IS [-3 , -2 , 0 ] + T [ -0.4 , 0.2 ,1]

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