91Ó°ÊÓ

Find the inverse of the matrix if it exists. $$\left[\begin{array}{ll} 3 & 4 \\ 7 & 9 \end{array}\right]$$

State the dimension of the matrix. $$\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]$$

Write the form of the partial fraction decomposition of the function (as in Example 4 ). Do not determine the numerical values of the coefficients. $$\frac{x^{4}+x^{2}+1}{x^{2}\left(x^{2}+4\right)^{2}}$$

Graph the inequality. $$3 x+4 y+12>0$$

Find the determinant of the matrix, if it exists. $$\left[\begin{array}{ll} \frac{1}{2} & \frac{1}{8} \\ 1 & \frac{1}{2} \end{array}\right]$$

Use back-substitution to solve the triangular system. $$\left\\{\begin{aligned} 2 x-y+6 z &=5 \\ y+4 z &=0 \\ -2 z &=1 \end{aligned}\right.$$

Use the elimination method to find all solutions of the system of equations. $$\left\\{\begin{aligned} 3 x^{2}-y^{2} &=11 \\ x^{2}+4 y^{2} &=8 \end{aligned}\right.$$

Graph the inequality. $$4 x+5 y<20$$

Write the form of the partial fraction decomposition of the function (as in Example 4 ). Do not determine the numerical values of the coefficients. $$\frac{x^{3}+x+1}{x(2 x-5)^{3}\left(x^{2}+2 x+5\right)^{2}}$$

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. $$\left[\begin{array}{rrr} 1 & 0 & -3 \\ 0 & 1 & 5 \end{array}\right]$$