(1) X1-3X2 + X3 = 1 list free x1 + 4x2-2x3 = 1 5x1-8x2 +2x3 = 5 6. Use Gauss-Jor

Question

(1) X1-3X2 + X3 = 1 list free x1 + 4x2-2x3 = 1 5x1-8x2 +2x3 = 5 6. Use Gauss-Jordan reduction to solve each of the ent on nt. following systems. (a) x1+X2=-1 4x1-3x2 = 3 (b) x1 + 3x2+X3+ x4= 3 re 2x1-2x2 + x3 + 2x4 = 3x1 + x2 + 2x3- x4=-1 (c) X1+X2+X3=0 (d) xi + X2+X3+ X4=0 2x1 + x2-x3 + 3x4 = 0 7. Give a geometric explanation of why a homogen- eous linear system consisting of two equations in three unknowns must have infinitely many solu- tions. What are the possible numbers of solutions of a nonhomogeneous 2 x 3 linear system? Give a

Explanation / Answer

(6c)

Augmented matrix for system of equations

Your matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by -2

Eliminate the 2nd column

Solution set:

x1 = 0

x2 = - t

x3 = t , t =parameter

(6d)

Augmented matrix for given system of equations

Your matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row (inversing the sign in the whole row)

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 9

Eliminate the 3rd column

Hide solution

Solution set:

x1 = - (4/3)t

x2 = 0

x3 = (1/3)t

x4 = t

and t = parameter(free)

X1 X2 X3 b 1 1 1 1 0 2 1 -1 -1 0

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