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someone helped me before but the answer they give was diffcult to understand and

ID: 3108284 • Letter: S

Question

someone helped me before but the answer they give was diffcult to understand and it wasn't right. they did it with cross product...

Determine whether the given (2X3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, given equations of the form x = at + b, y = ct + d, z = et + f

#1: x(1) + 2x(2) - x(3) = 2
x(1) + x(2) + x(3) = 3

* the numbers in the () are supposed to subscripts.

The books gives this as the answer : x(1) = -3t + 4
x(2) = 2t - 1
x(3) = t

Explanation / Answer

The reduced row echelon form of the augmented matrix is

which corresponds to the system

No equation of this system has a form zero = nonzero; Therefore, the system is consistent.

The leading entries in the matrix have been highlighted in yellow.

A leading entry on the (i,j) position indicates that the j-th unknown will be determined using the i-th equation.

Those columns in the coefficient part of the matrix that do not contain leading entries, correspond to unknowns that will be arbitrary. The system has infinitely many solutions:

Step 1: Transform the augmented matrix to the reduced row echelon form  (Hide details)