Construct the augmented matrix that corresponds to the following systems of equation. See the earlier example. (Answers may appear in slightly different, but equivalent, forms.)

$$\left\{\begin{array}{r}4 x+5 y-3 z=8 \\ 7 x-2 y+9=3 \\ 5 x-6 y+3 z=0\end{array}\right.$$

Use the method of substitution to solve the following system of equation. If a system is dependent, express the solution set in terms of one of the variables. See the earlier examples.

$$\left\{\begin{aligned} 4 x-y & =-1 \\ -8 x+2 y & =2\end{aligned}\right.$$

Determine values of the variables that will make the following equation true, if possible.

$$\left[\begin{array}{lll}4 x & 2 y^2 & z\end{array}\right]=\left[\begin{array}{l}12 \\ 18 \\ -2\end{array}\right]$$

Use graphing to guess the real solution(s) of the following systems, and then verify your answer algebraically. See the earlier examples.

$$\left\{\begin{array}{l}(x-2)^2+y^2=4 \\ (x+2)^2+y^2=4\end{array}\right.$$

Solve for x by finding the determinant.

$$\left|\begin{array}{cc}x-2 & 2 \\ 2 & x+1\end{array}\right|=0$$

Determine the values of the variables that will make the following equation true, if possible. See the earlier examples.

$$\left[\begin{array}{lll}a & 2 b & c\end{array}\right]+3\left[\begin{array}{lll}a & 2 & -c\end{array}\right]=\left[\begin{array}{lll}8 & 2 & 2\end{array}\right]$$

Construct the augmented matrix that corresponds to the following systems of equation. See the earlier example. (Answers may appear in slightly different, but equivalent, forms.)

$$\left\{\begin{aligned} \frac{12 x-1}{5}+\frac{y}{2} & =\frac{3 z}{2} \\ y-(x+3 z) & =-(1-y) \\ 2 x-2-z-2 y & =7 x\end{aligned}\right.$$

Given

$$A=\left[\begin{array}{cc}3 & -2 \\ 1 & 0 \\ 0 & 5\end{array}\right], B=\left[\begin{array}{cc}4 & -5 \\ 3 & 0 \\ -2 & 2\end{array}\right], C=\left[\begin{array}{cc}2 & -1 \\ 6 & 10 \\ -3 & 7\end{array}\right]$$

, and

$$D=\left[\begin{array}{ccc}3 & 2 & 5 \\ -2 & -4 & 1\end{array}\right]$$

, determine the following, if possible. See the earlier examples.

$$2(A-3 B)$$

Use the method of substitution to solve the following system of equation. If a system is dependent, express the solution set in terms of one of the variables. See the earlier examples.

$$\left\{\begin{array}{r}3 x+y=4 \\ -2 x+3 y=1\end{array}\right.$$

Use graphing to guess the real solution(s) of the following systems, and then verify your answer algebraically. See the earlier examples.

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

Determine values of the variables that will make the following equation true, if possible.

$$\left[\begin{array}{cc}w & 5 x \\ 2 y & z\end{array}\right]-3\left[\begin{array}{cc}w & x \\ 2 & -z\end{array}\right]=\left[\begin{array}{cc}4 & 2 \\ y-3 & -16\end{array}\right]$$

Write each of the following systems of equation as a single matrix equation. See the earlier example.

$$\left\{\begin{array}{r}2 x_1-3 x_3=7 \\ x_2-10 x_3=0 \\ 2 x_1-x_2+x_3=1\end{array}\right.$$

Evaluate the following determinant. See the earlier example.

$$\left|\begin{array}{cc}2 y & 3 x \\ y-1 & x^2\end{array}\right|$$

Construct the augmented matrix that corresponds to the following systems of equation. See the earlier example. (Answers may appear in slightly different, but equivalent, forms.)

$$\left\{\begin{aligned} 2(z+3)-x+y & =z \\ -3(x-2 y)-1 & =5 z \\ \frac{x}{3}-(y-2 z) & =x\end{aligned}\right.$$