91Ó°ÊÓ

1) A column-reduced matrix is a matrix transformed into a simplified form by applying operations on its columns with the objective of creating the identity matrix, if possible. The primary operations include multiplying a column by a nonzero constant, adding or subtracting a multiple of one column to another, and interchanging two columns. Example: Given matrix \( A = \begin{bmatrix} 2 & 3 \\ 6 & 9 \end{bmatrix} \), its column-reduced form is \( A = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} \). 2) A column-reduced echelon form matrix is a specific type of column-reduced matrix that satisfies certain conditions related to pivots (the first nonzero number in any nonzero column) and the position of zeros. Example: Given matrix \( B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \), its column-reduced echelon form is \( B = \begin{bmatrix} 1 & -4 & 1 \\ 4 & -13 & 1 \\ 7 & -22 & 1 \end{bmatrix} \).