Exam 47: Matrices and Systems of Equations

Write the augmented matrix for the system of linear equations. $\left\{ \begin{aligned}x + 7 y + 7 z & = - 6 \\3 y + 3 z & = 6 \\x + 7 z & = - 7\end{aligned} \right.$

Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices. $\left\{ \begin{aligned}x - y - 6 z & = - 33 \\y + 3 z & = 18 \\z & = 4\end{aligned} \right.$ $\left\{ \begin{array} { r l r } x - 7 y - 3 z & = - 57 \\y - 9 z & = - 30 \\z & = 4\end{array} \right.$

Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices. $\left\{ \begin{aligned}x + 2 y - 4 z & = - 8 \\y - 7 z & = 4 \\z & = - 1\end{aligned} \right.$ $\left\{ \begin{aligned}x - y - 5 z & = 21 \\y - 6 z & = 3 \\z & = - 1\end{aligned} \right.$

Fill in the blank(s)using elementary row operations to form a row-equivalent matrix.​ $\left[ \begin{array} { c c c } 1 & 1 & 1 \\5 & - 2 & 4\end{array} \right]$ $\left[ \begin{array} { c c c } 1 & 1 & 1 \\0 & \cdots & - 1\end{array} \right]$

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. ) $\left[\begin{array}{rrrrrr}1 & 2 & 5 & \vdots & 34 \\0 & 1 & 2 & \vdots & 14 \\0 & 0 & 1 & \vdots & 5\end{array}\right]$