Solve the system graphically or algebraically. Explain your choice of method.

$$\left\{\begin{aligned} x y-1 &=0 \\ -5 x-2 y+1 &=0 \end{aligned}\right.$$

In given exercise, the matrix product A X performs the translation of the point (x, y) to the point (x+h, y+k), when

$$A=\left[\begin{array}{lll} 1 & 0 & h \\ 0 & 1 & k \\ 0 & 0 & 1 \end{array}\right] \text { and } X=\left[\begin{array}{c} x \\ y \\ 1\end{array}\right]$$

Find $A^{-1}$ .

$$A=\left[\begin{array}{rrr}1 & 0 & -2 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right], \quad X=\left[\begin{array}{r}1 \\ -2 \\ 1\end{array}\right]$$

Find the point of equilibrium of the demand and supply equations. The point of equilibrium is the price $p$ and the number of units x that satisfy both the demand and supply equations. Demand $p=500-0.4 x$ Supply $p=380+0.1 x$

In given exercise, the matrix product A X performs the translation of the point (x, y) to the point (x+h, y+k), when

$$A=\left[\begin{array}{lll} 1 & 0 & h \\ 0 & 1 & k \\ 0 & 0 & 1 \end{array}\right] \text { and } X=\left[\begin{array}{c} x \\ y \\ 1\end{array}\right]$$

Find B=A X .

$$A=\left[\begin{array}{rrr}1 & 0 & -2 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right], \quad X=\left[\begin{array}{r}1 \\ -2 \\ 1\end{array}\right]$$

Write the augmented matrix for the system of linear equations.

$$\left\{\begin{aligned}-x+y &=12 \\ 10 x &=-90 \end{aligned}\right.$$

In given exercise, the matrix product A X performs the translation of the point (x, y) to the point (x+h, y+k), when

$$A=\left[\begin{array}{lll} 1 & 0 & h \\ 0 & 1 & k \\ 0 & 0 & 1 \end{array}\right] \text { and } X=\left[\begin{array}{c} x \\ y \\ 1\end{array}\right]$$

Predict the coordinates of the translated point

$$A=\left[\begin{array}{rrr}1 & 0 & -2 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right], \quad X=\left[\begin{array}{r}1 \\ -2 \\ 1\end{array}\right]$$

In given exercise find a system of line a equations that has the given solution. (There are many correct answers.)

(3,-4)

Find a system of linear equations that has the given solution. (There are many correct answers.) $\left(-\frac{3}{4}, 12\right)$

In given exercise, the matrix product A X performs the translation of the point (x, y) to the point (x+h, y+k), when

$$A=\left[\begin{array}{lll} 1 & 0 & h \\ 0 & 1 & k \\ 0 & 0 & 1 \end{array}\right] \text { and } X=\left[\begin{array}{c} x \\ y \\ 1\end{array}\right]$$

What are the coordinates of the point (x, y) ?

$$A=\left[\begin{array}{rrr}1 & 0 & -2 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right], \quad X=\left[\begin{array}{r}1 \\ -2 \\ 1\end{array}\right]$$

Solve the system graphically or algebraically. Explain your choice of method.

$$\left\{\begin{array}{l} y=x^{3}-2 x^{2}+x-1 \\ y=-x^{2}+3 x-1 \end{array}\right.$$

(a) find the determinant of A, (b) find $A^{-1}$, (c) find det$(A^{-1})$, and (d) compare your results from parts (a) and (c). Make a conjecture based on your results.

$$A=\left[\begin{array}{ll}{5} & {-1} \\ {2} & {-1}\end{array}\right]$$

Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations, and solve the system.

$$\left\{\begin{array}{r} x+y+z=0 \\ 2 x+3 y+z=0 \\ 3 x+5 y+z=0 \end{array}\right.$$

Let A be a $2 \times 2$ matrix given by

$$A=\left[\begin{array}{ll}{x} & {0} \\ {0} & {y}\end{array}\right]$$

Use the determinant of A to determine the conditions under which $A^{−1}$ exists.

Use matrices to solve the system of equations, if possible. Use Gauss-Jordan elimination.

$$\left\{\begin{array}{r} x+y+4 z=5 \\ 2 x+y-z=9 \end{array}\right.$$