91Ó°ÊÓ

Perform the indicated row operations (independently of one another, not in succession) on the following augmented matrix. $$\left[\begin{array}{rrr|r}1 & -2 & 0 & -1 \\\2 & -8 & -2 & 1 \\\3 & 5 & 1 & 2\end{array}\right]$$ Multiply the second row by \(-\frac{1}{2}\).

Find the given minor and cofactor pertaining to the matrix $$\left[\begin{array}{rrr} -3 & 0 & 2 \\ 1 & 5 & -4 \\ 0 & 6 & 5 \end{array}\right]$$ \(M_{23}\) and \(C_{23}\)

Use elimination to solve each system of equations. Check your solution. $$\left\\{\begin{array}{r} 5 x-3 y=23 \\ x+y=-13 \end{array}\right.$$

Use matrix inversion to solve the system of equations. $$\left\\{\begin{array}{r}2 x-5 y=-7 \\\\-3 x+2 y=-6\end{array}\right.$$

Solving Systems of Equations Using Matrices. $$\left\\{\begin{array}{c}x+2 y-2 z=-7 \\ 2 x+5 y-2 z=-10 \\ x-2 y-3 z=-9\end{array}\right.$$

Apply elementary row operations to a matrix to solve the system of equations. If there is no solution, state that the system is inconsistent. $$\left\\{\begin{array}{l}-x+2 y-3 z=2 \\ 2 x+3 y+2 z=1 \\ 3 x+y+5 z=1\end{array}\right.$$

The perimeter of a rectangular garden is 80 feet and the area it encloses is 336 square feet. Find the length and width of the garden.

Find \(A^{2}\) (the product \(A A\) ) and \(A^{3}\) (the prod\(\left.u c t\left(A^{2}\right) A\right)\). $$A=\left[\begin{array}{rr}1 & 1 \\\\-1 & 2\end{array}\right]$$

In this set of exercises, you will use the method of solving linear systems using matrices to study real-world problems. The athletic director of a local high school is ordering equipment for spring sports. He needs to order twice as many baseballs as softballs. The total number of balls he must order is \(300 .\) How many of each type should he order?

The volume of a paper party hat, shaped in the form of a right circular cone, is \(36 \pi\) cubic inches. If the radius of the cone is one-fourth the height of the cone, find the radius and the height.