StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q13E

Expert-verifiedFound in: Page 35

Book edition
5th

Author(s)
Otto Bretscher

Pages
442 pages

ISBN
9780321796974

*Compute the products A***x in Exercises 13 through 15 using**

*paper and pencil. In each case, compute the product two ways: in terms of the columns of A and in terms of the rows of A.*

**13.**

**$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\mathbf{}\left[\begin{array}{c}7\\ 11\end{array}\right]$ **

The dot product $\mathrm{A}\overrightarrow{\mathrm{x}}\mathrm{of}\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{c}7\\ 11\end{array}\right]\mathrm{is}\left[\begin{array}{c}29\\ 65\end{array}\right]$

Find $A\overrightarrow{x}$in terms of rows of A.

$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{c}7\\ 11\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow 7\left[\begin{array}{c}1\\ 3\end{array}\right]+11\left[\begin{array}{c}2\\ 4\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\begin{array}{c}7\\ 21\end{array}\right]+\left[\begin{array}{c}22\\ 44\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\begin{array}{c}7+22\\ 21+44\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\begin{array}{c}29\\ 65\end{array}\right]$

Find $A\overrightarrow{x}$in terms of columns of A.

$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{c}7\\ 11\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\begin{array}{c}\left(1\right)\left(7\right)+\left(2\right)\left(11\right)\\ \left(3\right)\left(7\right)+\left(4\right)\left(11\right)\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\begin{array}{c}7+22\\ 21+44\end{array}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\begin{array}{c}29\\ 65\end{array}\right]$_{}

94% of StudySmarter users get better grades.

Sign up for free