Short Answer

***Compute the products Ax 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.
$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 7 \\ 11 \end{matrix}]$**

The dot product $A \vec{x} of [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 7 \\ 11 \end{matrix}] is [\begin{matrix} 29 \\ 65 \end{matrix}]$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:

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

$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 7 \\ 11 \end{matrix}] \Rightarrow 7 [\begin{matrix} 1 \\ 3 \end{matrix}] + 11 [\begin{matrix} 2 \\ 4 \end{matrix}] \Rightarrow [\begin{matrix} 7 \\ 21 \end{matrix}] + [\begin{matrix} 22 \\ 44 \end{matrix}] \Rightarrow [\begin{matrix} 7 + 22 \\ 21 + 44 \end{matrix}] \Rightarrow [\begin{matrix} 29 \\ 65 \end{matrix}]$

Step 2 :

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

$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 7 \\ 11 \end{matrix}] \Rightarrow [\begin{matrix} (1) (7) + (2) (11) \\ (3) (7) + (4) (11) \end{matrix}] \Rightarrow [\begin{matrix} 7 + 22 \\ 21 + 44 \end{matrix}] \Rightarrow [\begin{matrix} 29 \\ 65 \end{matrix}]$

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Linear Algebra With Applications

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Short Answer

***Compute the products Ax 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.
$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 7 \\ 11 \end{matrix}]$**

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Linear Algebra With Applications

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Short Answer

Compute the products Ax in Exercises 13 through 15 usingpaper 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.[1234] [711]

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***Compute the products Ax 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.
$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 7 \\ 11 \end{matrix}]$**