Chapter 2 - Matrix Algebra - 2.2 Exercises - Page 112: 27

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a) $row_i(A)=row_i(IA)$ is the $ith$ row of matrix $A$. Matrix multiplication $row_i(I)\cdot A$ is the $ith$ row of the identity matrix, whose $ith$ term is 1 and all other terms are 0. Thus, the product is the ith row of A. Also, $row_i(IA)=row_i(I)\cdot A$ For b and c, $A=\begin{bmatrix} row_1(A)\\ row_2(A)\\ row_3(A)\\ \end{bmatrix}$ b) $EA=\begin{bmatrix} 0&1&0\\ 1&0&0\\ 0&0&1\\ \end{bmatrix}\begin{bmatrix} row_1(A)\\ row_2(A)\\ row_3(A)\\ \end{bmatrix}=\begin{bmatrix} row_2(A)\\ row_1(A)\\ row_3(A)\\ \end{bmatrix}$ c) $EA=\begin{bmatrix} 1&0&0\\ 0&1&0\\ 0&0&5\\ \end{bmatrix}\begin{bmatrix} row_1(A)\\ row_2(A)\\ row_3(A)\\ \end{bmatrix}=\begin{bmatrix} row_1(A)\\ row_2(A)\\ 5*row_3(A)\\ \end{bmatrix}$