Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.2 Matrix Algebra - Problems - Page 137: 37

Answer

See answer below

Work Step by Step

if A is an $n × p$ matrix and $D = diag(d_1,d_2,...,d_n)$ then $(DA)_{ij}=\sum \limits_{k=1}d_i \delta _{ik} a_{kj}=d_i\delta_{ii}a_{ij}=d_ia_{ij}$ Therefore, DA is the matrix obtained by multiplying the i-th row vector of $A$ by $d_i$, where $1\leq i \leq n$.
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