Solve the system. Assume that the variables are named x1,x2,… from left to right. ⎡⎣100010001−73182−5⎤⎦

nicekikah

nicekikah

Answered question

2021-09-29

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given reduced row echelon form. Solve the system. Assume that the variables are named x1,x2,… from left to right.

[100780103200115]

Answer & Explanation

smallq9

smallq9

Skilled2021-09-30Added 106 answers

The linear system corresponding to the augmented matrix is
x17x4=8
x2+3x4=2
x3+x4=5
The lending variables are x1,x2andx3. Solve for the leading variables: x1=8+7x4
x2=23x4
x3=5x4
Assign arbitrary value to free variable x4, say x4=t. Then the solution set is described by the parametric equations
x1=8+7t,x2=23t,x3=5t,x4=t

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