In addition to multiplying a matrix by a scalar, we can multiply two matrices. Finding the product of two matrices is only possible when the inner dimensions are the same, meaning that the number of columns of the first matrix is equal to the number of rows of the second matrix. If the inner dimensions do not match, the product is not defined. The process of matrix multiplication becomes clearer when working a problem with real numbers.
We now turn our attention to a special type of matrix called an elementary matrix. An elementary matrix is always a square matrix. Recall the row operations given in Definition [def:rowoperations]. You may construct an elementary matrix from any row operation, but remember that you can only apply one operation. Those which involve switching rows of the identity matrix are called permutation matrices. Elementary matrices can be used in place of row operations and therefore are very useful.
SOLUTION: factor the matrix A into a product of elementary matrices. A= [1 1] [2 1]
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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Please explain this in detail because i simply cannot understand previous explanations I have read for this type of problem. By the way this is from elementary linear algebra 10th edition section 1.