행렬 전체 문제

In the following exercises, solve each system of equations using a matrix.

$\left\{\begin{array}{l}-x-3y+2z=14 \\ -x+2y-3z=-4 \\ 3x+y-2z=6\end{array}\right.$

In the following exercises, solve each system of equations using a matrix.

$\left\{\begin{array}{l}x+y-3z=-1 \\ y-z=0 \\ -x+2y=1\end{array}\right.$

In the following exercises, solve each system of equations using a matrix.

$\left\{\begin{array}{l}x+2y+z=4 \\ x+y-2z=3 \\ -2x-3y+z=-7\end{array}\right.$

Solve the system of equations $\left\{\begin{array}{l}x+y=10 \\ x-y=6\end{array}\right.$ ⓐ by graphing and ⓑ by substitution. ⓒ Which method do you prefer? Why?

Solve the system of equations $\left\{\begin{array}{l}3x+y=12 \\ x=y-8\end{array}\right.$ by substitution and explain all your steps in words.

Simplify: $5(-2)-(-4)(1).$

Simplify: $-3(8-10)+(-2)(6-3)-4(-3-(-4)).$

Simplify: $\frac{-12}{-8}.$

Evaluate the determinant of ⓐ $\left[\begin{array}{c}4\quad -2 \\ 3\quad -1\end{array}\right]$ ⓑ $\left[\begin{array}{cccc}-3 & & & -4 \\ -2 & & & 0\end{array}\right].$

Evaluate the determinant of ⓐ $\left[\begin{array}{c}5\quad -3 \\ 2\quad -4\end{array}\right]$ ⓑ $\left[\begin{array}{cccc}-4 & & & -6 \\ 0 & & & 7\end{array}\right].$

Evaluate the determinant of ⓐ $\left[\begin{array}{c}-1\quad 3 \\ -2\quad 4\end{array}\right]$ ⓑ $\left[\begin{array}{cccc}-7 & & & -3 \\ -5 & & & 0\end{array}\right].$

For the determinant $|\begin{array}{ccccccc}4 & & & -2 & & & 3 \\ 1 & & & 0 & & & -3 \\ -2 & & & -4 & & & 2\end{array}|,$ find and then evaluate the minor of ⓐ ${a}_{1}$ ⓑ ${b}_{3}$ ⓒ ${c}_{2}.$

For the determinant $|\begin{array}{ccccccc}1 & & & -1 & & & 4 \\ 0 & & & 2 & & & -1 \\ -2 & & & -3 & & & 3\end{array}|,$ find and then evaluate the minor of ⓐ ${a}_{1}$ ⓑ ${b}_{2}$ ⓒ ${c}_{3}.$

For the determinant $|\begin{array}{ccccccc}-2 & & & -1 & & & 0 \\ 3 & & & 0 & & & -1 \\ -1 & & & -2 & & & 3\end{array}|,$ find and then evaluate the minor of ⓐ ${a}_{2}$ ⓑ ${b}_{3}$ ⓒ ${c}_{2}.$

Evaluate the determinant $|\begin{array}{ccccccc}2 & & & -3 & & & -1 \\ 3 & & & 2 & & & 0 \\ -1 & & & -1 & & & -2\end{array}|$ by expanding by minors along the first row.

Evaluate the determinant $|\begin{array}{ccccccc}3 & & & -2 & & & 4 \\ 0 & & & -1 & & & -2 \\ 2 & & & 3 & & & -1\end{array}|,$ by expanding by minors along the first row.

Evaluate the determinant $|\begin{array}{ccccccc}3 & & & -2 & & & -2 \\ 2 & & & -1 & & & 4 \\ -1 & & & 0 & & & -3\end{array}|,$ by expanding by minors along the first row.

Evaluate the determinant $|\begin{array}{ccccccc}4 & & & -1 & & & -3 \\ 3 & & & 0 & & & 2 \\ 5 & & & -4 & & & -3\end{array}|$ by expanding by minors.

Evaluate the determinant $|\begin{array}{ccccccc}2 & & & -1 & & & -3 \\ 0 & & & 3 & & & -4 \\ 3 & & & -4 & & & -3\end{array}|$ by expanding by minors.

Evaluate the determinant $|\begin{array}{ccccccc}-2 & & & -1 & & & -3 \\ -1 & & & 2 & & & 2 \\ 4 & & & -4 & & & 0\end{array}|$ by expanding by minors.