The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. begin{bmatrix}1&-2&0&0&-30&0&1&0&-40&0&0&1&5end{bmatrix}

waigaK 2020-12-24 Answered
The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. [120030010400015]
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wornoutwomanC
Answered 2020-12-25 Author has 81 answers
The augmented matrix does not contain a row in which the only nonzero entry appears in the last column. Therefore, this system of equations must be consistent. Convert the augmented matrix into a system of equantions. {x12x2=3x3=4x4=5
Solve for the leading entry for each individual equation. Determine thee free variables, if any. x1=3+2x2
x2, free
x3=4
x4=5
Parameterize the free variables. {x1=3+2x2x2=tx3=4x4=5
Write the solution in vector form. x=[3045]+t[2100]
Result: consistent: x=[3045]+t[2100]
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