91Ó°ÊÓ

Find the determinant of the matrix, if it exists. $$\left[\begin{array}{rr} \frac{3}{2} & 1 \\ -1 & -\frac{2}{3} \end{array}\right]$$

State the dimension of the matrix. $$\left[\begin{array}{l} 12 \\ 35 \end{array}\right]$$

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

Find the determinant of the matrix, if it exists. $$\left[\begin{array}{rr} 0.2 & 0.4 \\ -0.4 & -0.8 \end{array}\right]$$

State the dimension of the matrix. $$\left[\begin{array}{r} -3 \\ 0 \\ 1 \end{array}\right]$$

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

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

Use back-substitution to solve the triangular system. \(\left\\{\begin{aligned} 3 x-3 y+z &=0 \\ y+4 z &=10 \\ z &=3 \end{aligned}\right.\)

Find the values of \(a\) and \(b\) that make the matrices \(A\) and \(B\) equal. $$A=\left[\begin{array}{rrr} 3 & 5 & 7 \\ -4 & a & 2 \end{array}\right] \quad B=\left[\begin{array}{rrr} 3 & 5 & b \\ -4 & -5 & 2 \end{array}\right]$$

A system of inequalities and several points are given. Determine which points are solutions of the system. $$\left\\{\begin{array}{rl} x+2 y & \geq 4 \\ 4 x+3 y & \geq 11 \end{array} ; \quad(0,0),(1,3),(3,0),(1,2)\right.$$