Boost Your Understanding of Linear Equation Forms

$(792)(5.19\times {10}^{-}5)$

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system by back substitution. Assume that the variables are named$x_1,x_2,\dots$ from left to right.
$\left[\begin{array}{cccc}1& -3& 7& 1\\ 0& 1& 4& 0\\ 0& 0& 0& 1\end{array}\right]$

Write the vector form of the general solution of the given system of linear equations.
$x_1+4x_4=0$
$x_2-2x_4$

Solve the system by clennaton

$\{\begin{array}{l}2x-y=0\\ 3x-2y=-3\end{array}$
The solution is____

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 $x_1,x_2,$… from left to right.

$\left[\begin{array}{ccccc}1& 0& 0& -7& 8\\ 0& 1& 0& 3& 2\\ 0& 0& 1& 1& -5\end{array}\right]$

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.

$\left[\begin{array}{cccc}1& -2& 0& -4\\ 0& 0& 1& 3\\ 0& 0& 0& 0\end{array}\right]$

Reduce the system of linear equations to upper triangular form and solve.
$\{\begin{array}{l}3x-y=1\\ -3x+y=4\end{array}$

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.

$\left[\begin{array}{ccc}1& -2& 6\\ 0& 0& 0\end{array}\right]$

The row echelon form of a system of linear equations is given.
(a)Writethesystemofequationscorrespondingtothegivenmatrix.Use x,y.or x,y,z.or $x_1,x_2,x_3,x_4$ asvariables.
(b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution. $\left[\begin{array}{cccc}1& -3& |& -4\\ 0& 1& |& 0\end{array}\right]$

Reduce the system of linear equations to upper triangular form and solve.
$\{\begin{array}{l}2x-y=3\\ x-3y=7\end{array}$

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Tell whether the system has one solution, no solution, or infinitely many solutions. Write the solutions or, if there is no solution, say the system is inconsistent.

$\left[\begin{array}{ccccc}1& 0& -2& |& 6\\ 0& 1& 3& |& 1\end{array}\right]$

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system by back substitution. Assume that the variables are named $x_1,x_2,\dots$from left to right. $\left[\begin{array}{ccccc}1& 0& 5& 3& 2\\ 0& 1& -2& 4& -7\\ 0& 0& 1& 1& 3\end{array}\right]$

The row echelon form of a system of linear equations is given.
(a)Writethesystemofequationscorrespondingtothegivenmatrix.Usex,y.or x,y,z.or $x_1,x_2,x_3,x_4$ asvariables.
(b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution.

$\left[\begin{array}{cccc}1& 2& |& 5\\ 0& 1& |& -1\end{array}\right]$

Each of the matrices is the final matrix form for a system of two linear equations in the variables x1 and x2. Write the solution of the system.

$\left[\begin{array}{cccc}1& 0& |& 3\\ 0& 1& |& -5\end{array}\right]$

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.

$\left[\begin{array}{ccc}1& -4& 5\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

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 $x_1,x_2,\dots x,\dots$ from left to right.

$\left[\begin{array}{cccc}1& 0& 0& -3\\ 0& 1& 0& 0\\ 0& 0& 1& 7\end{array}\right]$