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To expand a matrix in terms of its rows and columns, we need to first identify the dimensions of the matrix. Once we have done that, we can then proceed to apply the expansion methods to each row and column of the matrix separately. One way of doing this is to use the elementary row and column operations, which allow us to add, subtract, or multiply rows and columns of the matrix in order to obtain a matrix that is in row-echelon or reduced row-echelon form. Another way of expanding a matrix is to use the Kronecker product, which allows us to combine two matrices of different sizes into a larger matrix with more rows and columns. This method is particularly useful in the context of linear algebra and matrix computations, where we often need to transform, manipulate, or combine matrices in various ways in order to solve problems or perform calculations.