## Linear Algebra and Its Applications, Review Exercise 1.21

Review exercise 1.21. Given the 2 by 2 matrix $D = \begin{bmatrix} 2&0 \\ 0&5 \end{bmatrix}$

describe the rows of $DA$ and the columns of $AD$.

Answer: When multiplying $A$ from the left by $D$ to produce $DA$ the first row of $DA$ will be 2 times the first row of $A$ and the second row of $DA$ will be 5 times the second row of $A$. For example $\begin{bmatrix} 2&0 \\ 0&5 \end{bmatrix} \begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} = \begin{bmatrix} 2&4 \\ 15&20 \end{bmatrix}$

When multiplying $A$ from the right by $D$ to produce $AD$ the first column of $AD$ will be 2 times the first column of $A$ and the second column of $AD$ will be 5 times the second column of $A$. For example $\begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} \begin{bmatrix} 2&0 \\ 0&5 \end{bmatrix} = \begin{bmatrix} 2&10 \\ 6&20 \end{bmatrix}$

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition , Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books .

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