Solve the system of linear equations. (Enter your answers as a comma-separated l

Question

Solve the system of linear equations. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x_3 = t and solve for x_1 and x_2 in terms of t.) 3x_1 - 2x_2 + 4x_3 = 1 x_1 + x_2 - 2x_3 = 3 2x_1 - 3x_2 + 6x_3 = 8 (x_1, x_2, x_3) = () Find the solution set of the system of linear equations represented by the augmented matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x_4 = t and solve for x_1, x_2, and x_3 in terms of t.) [1 0 0 0 2 1 0 0 0 2 1 0 1 1 2 1 5 6 4 5] (x_1, x_2, x_3, x_4) = ()

Explanation / Answer

Solution:

3. First we set up agumented matrix such that Ax = B

and transform this matrix [A : B ] in row echelon form using elementry operation

As we can see that our reduced matrix is

which is pivot in only first two column

therefore

system has infinite number of solution

let free variable x3 = t

now

1

we get from matrix

x1 = 0

x2 -2x3 = 0

x2 = 2x3

x2 = 2t ( x3 = t)

Answer: (x1 , x2 ,x3 ) = ( 0 ,2t , t)

Row
Operation
1:   3 -2 4 1 1 1 -2 3 2 -3 6 8 multiply the 1st row by 1/3 1 -2/3 4/3 1/3 1 1 -2 3 2 -3 6 8

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