A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the
System, if one exists.
A) , , for any real number z.
B) , , for any real number z.
C) , , for any real number z.
D) , , for any real number z.
E)no solution

Question

A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the ​
System, if one exists.   ​
A) , , for any real number z. 
B) , , for any real number z. 
C) , , for any real number z. 
D) , , for any real number z. 
E)no solution

Quizplus · Accepted Answer

The reduced matrix is in row echelon form with a leading 1 in the first column of the first row. This means that the first variable (x) is a leading variable and the second variable (y) is a free variable. The last row of the reduced matrix corresponds to the equation 0z = 0, which is always true for any value of z.

Using back substitution, we can find the values of x and y in terms of z:

x + 2y = 3 
x = 3 - 2y 
y = y

Therefore, the general solution is:

x = 3 - 2z 
y = z

A System of Linear Equations and a Reduced Matrix for the System