MATH 305 Lecture Notes - Lecture 9: Elementary Matrix, Identity Matrix
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3. (scaling) multiply a row by a nonzero constant (replacement) replace one row by a multiple of another row + itself (interchange) interchange two rows. Definition: an elementary matrix is a matrix that results from performing a single row operation on an identity matrix. Theorem 4. 2. 1: let e be an elementary matrix corresponding to a particular row operation on i m, and let a be an m n matrix. Then the product ea is the matrix that results from applying this same row operation to a. (left multiply e to a = row operations on a) Verify 4. 2. 1, perform the row operation 2r1 + r3. Theorem (add): let f be an elementary matrix corresponding to a particular column operation on i n, and let a be an m n matrix. Then the product af is the matrix that results from applying this same column operation to a. (right multiply f to a = column operations on a)