Exam 15: Systems of Equations: Matrices and Determinants

Solve the system by the substitution or elimination method. $\left( \begin{array} { r l r } x - y & = 3 \\x ^ { 2 } - y ^ { 2 } & = 45\end{array} \right)$

Solve the system. $\left( \begin{array} { r l l } 2 x &+ &2 y & -& z & =& - 2 \\&&5 x &-& 2 y & = & - 8 \\&&2 x &+& 5 y & = & - 9\end{array} \right)$

When the graphs for a system of two linear equations are parallel lines, then there is no solution.

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { r l l } \frac { 1 } { 2 } x &-& \frac { 1 } { 6 } y &= & - 1 \\\frac { 1 } { 2 } x &+ &\frac { 1 } { 4 } y &= & - 11\end{array} \right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( x , y ).

Indicate whether the matrix is in reduced echelon form. $\left. \left[ \begin{array} { c c c } 1 & 1 & 0 \\0 & 1 & 1 \\0 & 0 & 1\end{array} \right] \quad \begin{array} { c } - 10 \\2 \\- 3\end{array} \right]$ Enter yes or no .

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|$ -Third step

The matrix is in reduced echelon form. $\left. \left[ \begin{array} { c c c c } 1 & 0 & 0 & 4 \\0 & 1 & 0 & - 8 \\0 & 0 & 1 & 9 \\0 & 0 & 0 & 0\end{array} \right] \quad \begin{array} { c } 7 \\10 \\1 \\0\end{array} \right]$

The determinant D is calculated using the coefficients of the equations in the system of equations.