Problem 20
A matrix \(A\) is given below. In Exercises 16 20, a matrix \(B\) is given. Give the row operation that transforms \(A\) into \(B\). $$A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 2 & 3\end{array}\right]$$ $$B=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 1 \\ 0 & 2 & 2\end{array}\right]$$
Problem 20
In a basketball game, where points are scored either by a 3 point shot, a 2 point shot or a 1 point free throw, 110 points were scored from 70 successful shots. Find all ways in which the points may have been scored in this game.
Problem 21
Describe the equations of the linear functions that go through the point \((1,3) .\) Give 2 examples.
Problem 21
Rewrite the system of equations in matrix form. Find the solution to the linear system by simultaneously manipulating the equations and the matrix. $$ \begin{array}{l} x+y=3 \\ 2 x-3 y=1 \end{array} $$
Problem 21
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{llllll}2 & 2 & 1 & 3 & 1 & 4 \\ 1 & 1 & 1 & 3 & 1 & 4\end{array}\right]$$
Problem 22
Rewrite the system of equations in matrix form. Find the solution to the linear system by simultaneously manipulating the equations and the matrix. $$ \begin{array}{l} 2 x+4 y=10 \\ -x+y=4 \end{array} $$
Problem 22
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{cccccc}1 & -1 & 3 & 1 & -2 & 9 \\ 2 & -2 & 6 & 1 & -2 & 13\end{array}\right]$$
Problem 22
Describe the equations of the linear functions that go through the point \((2,5) .\) Give 2 examples.
Problem 23
Rewrite the system of equations in matrix form. Find the solution to the linear system by simultaneously manipulating the equations and the matrix. $$ \begin{array}{l} -2 x+3 y=2 \\ -x+y=1 \end{array} $$
Problem 24
Rewrite the system of equations in matrix form. Find the solution to the linear system by simultaneously manipulating the equations and the matrix. $$ \begin{array}{c} 2 x+3 y=2 \\ -2 x+6 y=1 \end{array} $$
