The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or \(x_1,x_2,x_3,x_4\) as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. \(\left[\begin{array}{cccc|c} 1&0&0&4&2\\0&1&1&3&3\\0&0&0&0&0 \end{array}\right]\)

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The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y. or x, y, z. or \(x_1, x_2, x_3, x_4\) as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. \(\begin{bmatrix}1 & 0 & 0 & 0 & 1\\ 0 &1 & 0 &0 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{bmatrix}\)

The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or \(x_1,x_2,x_3,x_4\) as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. \(\left[\begin{array}{ccc|c}{1} & {0} & {4} & {4} \\ {0} & {1} & {3} & {2} \\ {0} & {0} & {0} & {0}\end{array}\right]\)

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or \(x_1,x_2,x_3,x_4x\) as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. \(\begin{bmatrix}1&0&0&0&|&1 \\0&1&0&0&|&2 \\0&0&1&2&|&3 \end{bmatrix}\)

The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use \(x, y\); or \(x, y, z;\) or \(x_{1},x_{2},x_{3},x_{4} \) as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. \([1,0;1,0;5,-1]\)