Convert the system 3x1 5x2 -2 = 6x1 7x2 -1 to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions. Augmented matrix: Echelon form: Is the system consistent? select ( Solution: (x1, x2) = + + S1 Help: To enter a matrix use [[ 1. For example, to enter the 2 x 3 matrix 2 you would type [[1,2,3),(6,5,4]1, so each inside set of [) represents a row. If there is no free variable in the solution, then type 0 in each of the answer blanks directly before each s. For example, if the answer is (x,x2)= (5,-2), then you would enter (5 +0s1,-2 + 0s1). If the system is inconsistent, you do not have to type anything in the "Solution" answer blanks. I

Question

contestada

Respuesta :

steffaniasierrag steffaniasierrag · Answer 1 · 2019-10-06T16:32:25+02:00

Answer:

[tex]3x_1+5x_2=-2\\6x_1+7x_2=-1[/tex]

The augmented matrix associated to the linear system is

[tex]\left[\begin{array}{ccc}3&5&-2\\6&7&-1\end{array}\right][/tex]

Using row operations we reduce the system to echelon form:

1. We substract to the second row three times the first row and obtain the matrix

[tex]\left[\begin{array}{ccc}3&5&-2\\0&-3&3\end{array}\right][/tex] that is the echelon form of the system.

Now we use backward substitution to find the solution.

1. [tex]-3x_2=3\\x_2=-1[/tex]

2. [tex]3x_1+5x_2=-2\\3x_1+5(-1)=-2\\x_1=1[/tex]

The the unique solution is [tex](x_1,x_2)=(1,-1)[/tex]