Exam 9: Systems and Matrices

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { r r } 3 & - 1 \\5 & 5\end{array} \right] = \left[ \begin{array} { r r } x & - 1 \\y & z\end{array} \right]$

Solve the equation for x. - $\left| \begin{array} { r r } 3 & x \\2 & - 1\end{array} \right| = 7$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Provide an appropriate response. -Suppose that you are solving a system of 4 linear equations in 4 variables by the Gauss-Jordan method. If you use the transformation $- 2 R _ { 1 } + R _ { 4 }$ , which row or rows of the augmented matrix, if any, will change?

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r | r } 20 & 3 & 18 \\ 11 & 15 & 6 \end{array} \right]$

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } 8 & 3 \\ 2 & 4 \\ - 6 & - 4 \end{array} \right] + \left[ \begin{array} { r r } 5 & 9 \\ - 4 & 6 \\ - 2 & 3 \end{array} \right]$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=1 x+y=1

Solve the problem. -The sum of a studentʹs three scores is 218. If the first is 10 points more than the second, and the sum of the first two is 20 more than twice the third, what was the first score?

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=16 4x+y=-8

Graph the solution set of the system of inequalities. -

Find the value of the determinant. - $\left| \begin{array} { l l } \mathrm { a } & \mathrm { b } \\ \mathrm { b } & \mathrm { a } \end{array} \right|$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x-8y+z=6 3x-y+2z=7

The following graph shows the populations of the metropolitan areas of City X and City Y over six years. -In what years was the population of the City X metropolitan area less than that of the City Y metropolitan area?

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - -7x+9y=-54 2x-3y=18

Provide an appropriate response. -Suppose that $A$ and $B$ are two matrices such that $A + B , A - B$ , and $A B$ all exist. What can you conclude about the dimensions of $\mathrm { A }$ and $\mathrm { B }$ ?

Solve the system by using the inverse of the coefficient matrix. - 3x-y-9z=-68 -9x-3z=-30 2y+z=23

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } 9 & 4 \\ 4 & 4 \end{array} \right]$ and $\left[ \begin{array} { r r } - .2 & .2 \\ .2 & - .45 \end{array} \right]$

Solve the system by elimination. - x-6y=-43 -3x-7y=-46

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+y= ax+by=b

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l } 4 & 5 \\ 1 & 0 \end{array} \right]$