Linear Algebra (#15) Describe the solutions of the first system of equations bel

Question

Linear Algebra (#15)

Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations shown below. x_1 + 4x_2 - 7x_3 = 8 x_1 + 4x_2 - 7x_3 = 0 2x_1 + x_2 - 7x_3 = 23 2x_1 = x_2 - 7x_3 = 0 -x_1 + 3x_2 = -15 -x_1 + 3x_2 = 0 where the solution set is x = [x_1 x_2 x_3] Describe the solution set of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.) A. x = B. x = x_2 C. x = + x_3 D. x = x_2 + x_3 Which option best compares the two systems? A. The solution set of the first system is a plane parallel to the line that is the solution set of the second system. B. The solution set of the first system is a line perpendicular to the line that is the solution set of the second system. C. The solution set of the first system is a plane parallel to

Explanation / Answer

2x1 + x2 -7x3 = 23

-x1 + 3x2 = -15

or -2x1 +6x2 = -30

7x2 = -7+7x3

x2 = -1 + x3

x1 = 3x2 +15 = 3(-1 + x3) + 15 = 12 + 3 *x3

hence

(x1,x2,x3) = ( 12 + 3 *x3 ,  -1 + x3 , x3)

= (12,1,0) + x3 (3,1,1)

option D) is correct

note eqn 3) can be obtained from eqn 2) from eqn 1)

hence the line parallel to plane is right solution

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