Problem 17
A matrix \(A\) is given below. In Exercises 16 20, a matrix \(B\) is given. Give the row operation that transforms \(A\) into \(B\). $$A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 2 & 3\end{array}\right]$$ $$B=\left[\begin{array}{lll}1 & 1 & 1 \\ 2 & 1 & 2 \\ 1 & 2 & 3\end{array}\right]$$
Problem 17
State for which values of \(k\) the given system will have exactly 1 solution, infinite solutions, or no solution. $$ \begin{array}{l} x_{1}+2 x_{2}=1 \\ x_{1}+k x_{2}=2 \end{array} $$
Problem 18
In a football game, 29 points are scored from 8 scoring occasions. There are 2 more successful extra point kicks than successful two point conversions. Find all ways in which the points may have been scored in this game.
Problem 18
A matrix \(A\) is given below. In Exercises 16 20, a matrix \(B\) is given. Give the row operation that transforms \(A\) into \(B\). $$A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 2 & 3\end{array}\right]$$ $$B=\left[\begin{array}{lll}3 & 5 & 7 \\ 1 & 0 & 1 \\ 1 & 2 & 3\end{array}\right]$$
Problem 18
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{cccc}2 & -1 & 1 & 5 \\ 3 & 1 & 6 & -1 \\ 3 & 0 & 5 & 0\end{array}\right]$$
Problem 18
State for which values of \(k\) the given system will have exactly 1 solution, infinite solutions, or no solution. $$ \begin{array}{l} x_{1}+2 x_{2}=1 \\ x_{1}+3 x_{2}=k \end{array} $$
Problem 19
A matrix \(A\) is given below. In Exercises 16 20, a matrix \(B\) is given. Give the row operation that transforms \(A\) into \(B\). $$A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 2 & 3\end{array}\right]$$ $$B=\left[\begin{array}{lll}1 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 2 & 3\end{array}\right]$$
Problem 19
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{cccc}1 & 1 & -1 & 7 \\ 2 & 1 & 0 & 10 \\ 3 & 2 & -1 & 17\end{array}\right]$$
Problem 19
In a basketball game, where points are scored either by a 3 point shot, a 2 point shot or a 1 point free throw, 80 points were scored from 30 successful shots. Find all ways in which the points may have been scored in this game.
Problem 20
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{cccc}4 & 1 & 8 & 15 \\ 1 & 1 & 2 & 7 \\ 3 & 1 & 5 & 11\end{array}\right]$$
