Short Answer

Compute the products $A \vec{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
18. $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$

The product of $A \vec{x}$ is, $[\begin{matrix} 5 \\ 11 \\ 17 \end{matrix}]$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the given matrices

If $A$ is an $n \times m$ matrix with row vectors ${\vec{ω}}_{1}, . ...., {\vec{ω}}_{n}$ and $\vec{x}$ is a vector in $ℝ^{m}$ then, .

$A \vec{x} = [\begin{matrix} - {\vec{ω}}_{1} - \\ ⋮ \\ - {\vec{ω}}_{n} - \end{matrix}] \vec{x} = [\begin{matrix} - {\vec{ω}}_{1} \cdot \vec{x} - \\ ⋮ \\ - {\vec{ω}}_{n} \cdot \vec{x} - \end{matrix}]$

The given expression is,

$[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$

Here $A$ is $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}]$ and $\vec{x}$ is $[\begin{matrix} 1 \\ 2 \end{matrix}]$ .

Step 2: Perform the operation

Now, find the product by performing the row column operations as follow:

$\begin{matrix} [\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}] = [\begin{matrix} 1 \cdot 1 + 2 \cdot 2 \\ 3 \cdot 1 + 4 \cdot 2 \\ 5 \cdot 1 + 6 \cdot 2 \end{matrix}] \\ = [\begin{matrix} 5 \\ 11 \\ 17 \end{matrix}] \end{matrix}$

Hence, the required product is $[\begin{matrix} 5 \\ 11 \\ 17 \end{matrix}]$ .

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Linear Algebra With Applications

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Short Answer

Compute the products $A \vec{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
18. $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$

Step by Step Solution

Step 1: Consider the given matrices

Step 2: Perform the operation

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Linear Algebra With Applications

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Compute the products Ax→ in Exercises 16 through 19 using paper and pencil (if the products are defined).18. [123456][12]

Step by Step Solution

Step 1: Consider the given matrices

Step 2: Perform the operation

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Compute the products $A \vec{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
18. $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$