91Ó°ÊÓ

Choose h and k such that the augmented matrix shown has each of the following: (a) one solution (b) no solution (c) infinitely many solutions $$ \left[\begin{array}{ll|l} 1 & h & 2 \\ 2 & 4 & k \end{array}\right] $$

Choose h and \(k\) such that the augmented matrix shown has each of the following: (a) one solution (b) no solution (c) infinitely many solutions $$ \left[\begin{array}{ll|l} 1 & 2 & 2 \\ 2 & h & k \end{array}\right] $$

Determine if the system is consistent. If so, is the solution unique? $$ \begin{array}{c} x+2 y+z-w=2 \\ x-y+z+w=0 \\ 2 x+y-z=1 \\ 4 x+2 y+z=3 \end{array} $$

Determine which matrices are in reduced row-echelon form. (a) \(\left[\begin{array}{lll}1 & 2 & 0 \\ 0 & 1 & 7\end{array}\right]\) (b) \(\left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0\end{array}\right]\) (c) \(\left[\begin{array}{llllll}1 & 1 & 0 & 0 & 0 & 5 \\ 0 & 0 & 1 & 2 & 0 & 4 \\ 0 & 0 & 0 & 0 & 1 & 3\end{array}\right]\)

Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{rrrr} 2 & -1 & 3 & -1 \\ 1 & 0 & 2 & 1 \\ 1 & -1 & 1 & -2 \end{array}\right] $$

Exercise 1.2.21 Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{rrrr} 0 & 0 & -1 & -1 \\ 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & -1 \end{array}\right] $$

Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{rrrr} 3 & -6 & -7 & -8 \\ 1 & -2 & -2 & -2 \\ 1 & -2 & -3 & -4 \end{array}\right] $$

Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{rrrr} 2 & 4 & 5 & 15 \\ 1 & 2 & 3 & 9 \\ 1 & 2 & 2 & 6 \end{array}\right] $$

Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{rrrr} 4 & -1 & 7 & 10 \\ 1 & 0 & 3 & 3 \\ 1 & -1 & -2 & 1 \end{array}\right] $$

Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{llll} 3 & 5 & -4 & 2 \\ 1 & 2 & -1 & 1 \\ 1 & 1 & -2 & 0 \end{array}\right] $$Exercise 1.2.25 Row reduce the following matrix to obtain the row-echelon form. Then continue to obtain the reduced row-echelon form. $$ \left[\begin{array}{llll} 3 & 5 & -4 & 2 \\ 1 & 2 & -1 & 1 \\ 1 & 1 & -2 & 0 \end{array}\right] $$