91Ó°ÊÓ

Perform the matrix operation, or if it is impossible, explain why. $$\left[\begin{array}{lll} 2 & 1 & 2 \\ 6 & 3 & 4 \end{array}\right]\left[\begin{array}{rr} 1 & -2 \\ 3 & 6 \\ -2 & 0 \end{array}\right]$$

A matrix is given. (a) Determine whether the matrix is in row-echelon form. (b) Determine whether the matrix is in reduced row-echelon form. (c) Write the system of equations for which the given matrix is the augmented matrix. $$\left[\begin{array}{rrr} 1 & 3 & -3 \\ 0 & 1 & 5 \end{array}\right]$$

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 3. $$\left\\{\begin{array}{l} x-y=3 \\ x+3 y=7 \end{array}\right.$$

Find the determinant of the matrix, if it exists. $$\left[\begin{array}{rr} 2.2 & -1.4 \\ 0.5 & 1.0 \end{array}\right]$$

Use back-substitution to solve the triangular system. $$\left\\{\begin{aligned} x-2 y+3 z &=10 \\ 2 y-z &=2 \\ 3 z &=12 \end{aligned}\right.$$

Express the rule in function notation. (For example, the rule "square, then subtract 5 " is expressed as the function \(f(x)=x^{2}-5\). Take the square root, add \(8,\) then multiply by \(\frac{1}{3}\)

Use the substitution method to find all solutions of the system of equations. $$\left\\{\begin{aligned}x^{2}-y &=1 \\\2 x^{2}+3 y &=17\end{aligned}\right.$$

Express the function (or rule) in words. $$h(x)=x^{2}+2$$

Use the elimination method to find all solutions of the system of equations. $$\left\\{\begin{array}{r}x+2 y=5 \\\2 x+3 y=8\end{array}\right.$$

A matrix is given. (a) Determine whether the matrix is in row-echelon form. (b) Determine whether the matrix is in reduced row-echelon form. (c) Write the system of equations for which the given matrix is the augmented matrix. $$\left[\begin{array}{llll} 1 & 2 & 8 & 0 \\ 0 & 1 & 3 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$$