91Ó°ÊÓ

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. $$ \left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 3 \end{array}\right] $$

Find the inverse of the matrix (if it exists). $$ \left[\begin{array}{lll} 1 & 1 & 1 \\ 3 & 5 & 4 \\ 3 & 6 & 5 \end{array}\right] $$

Use a determinant to determine whether the points are collinear. $$ (-2,-11),(4,13),(2,5) $$

Find all (a) minors and (b) cofactors of the matrix. $$ \left[\begin{array}{rr} 3 & 4 \\ 2 & -5 \end{array}\right] $$

Solve for \(X\) when $$A=\left[\begin{array}{rr} -2 & -1 \\ 1 & 0 \\ 3 & -4 \end{array}\right] \text { and } B=\left[\begin{array}{rr} 0 & 3 \\ 2 & 0 \\ -4 & -1 \end{array}\right].$$ $$ X=3 \dot{A}-2 \bar{B} $$

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. $$ \left[\begin{array}{llllll} \mathbf{1} & \underline{3} & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 8 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 \end{array}\right] $$

Find all (a) minors and (b) cofactors of the matrix. $$ \left[\begin{array}{rr} 11 & 0 \\ -3 & 2 \end{array}\right] $$

Find the inverse of the matrix (if it exists). $$ \left[\begin{array}{rrr} 1 & 2 & 2 \\ 3 & 7 & 9 \\ -1 & -4 & -7 \end{array}\right] $$

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. $$ \left[\begin{array}{llll} 1 & 0 & 0 & 10 \\ 0 & 1 & 3 & 9 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right] $$

Solve for \(X\) when $$A=\left[\begin{array}{rr} -2 & -1 \\ 1 & 0 \\ 3 & -4 \end{array}\right] \text { and } B=\left[\begin{array}{rr} 0 & 3 \\ 2 & 0 \\ -4 & -1 \end{array}\right].$$ $$ 2 X=2 A-B $$