Short Answer

Give an example of a linear transformation whose image is the line spanned by $[\begin{matrix} 7 \\ 6 \\ 5 \end{matrix}]$ in $ℝ^{3}$ .

$[\begin{matrix} 7 & 0 & 0 \\ 6 & 0 & 0 \\ 5 & 0 & 0 \end{matrix}]$ is a linear transformation whose image is the line spanned by $[\begin{matrix} 7 \\ 6 \\ 5 \end{matrix}]$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the parameters.

$7 x + 6 y + 5 z = 0$ The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

$i m a g e (f) = \{f (x) : x i n X\} = \{b i n Y : b = f (x), f o r s o m e x i n X\}$

Consider the system in terms of an equation,

Thus, $[\begin{matrix} 7 & 0 & 0 \\ 6 & 0 & 0 \\ 5 & 0 & 0 \end{matrix}]$ is a linear transformation.

Step 2: Final answer.

$[\begin{matrix} 7 & 0 & 0 \\ 6 & 0 & 0 \\ 5 & 0 & 0 \end{matrix}]$ is a linear transformation whose image is the line spanned by $[\begin{matrix} 7 \\ 6 \\ 5 \end{matrix}]$ .

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Linear Algebra With Applications

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Short Answer

Give an example of a linear transformation whose image is the line spanned by $[\begin{matrix} 7 \\ 6 \\ 5 \end{matrix}]$ in $ℝ^{3}$ .

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Final answer.

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Give an example of a linear transformation whose image is the line spanned by [765] in ℝ3 .

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Step 1: Consider the parameters.

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Give an example of a linear transformation whose image is the line spanned by $[\begin{matrix} 7 \\ 6 \\ 5 \end{matrix}]$ in $ℝ^{3}$ .