In Exercises, column vectors are written as rows, such as

Chapter 1, Problem 32E

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QUESTION:

In Exercises, column vectors are written as rows, such as \(\mathbf{x}=\left(x_{1}, x_{2}\right)\), and T(x) is written as \(T\left(x_{1}, x_{2}\right)\).

Show that the transformation T defined by \(T\left(x_{1}, x_{2}\right)=\left(4 x_{1}-2 x_{2}, 3\left|x_{2}\right|\right)\) is not linear.

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QUESTION:

In Exercises, column vectors are written as rows, such as \(\mathbf{x}=\left(x_{1}, x_{2}\right)\), and T(x) is written as \(T\left(x_{1}, x_{2}\right)\).

Show that the transformation T defined by \(T\left(x_{1}, x_{2}\right)=\left(4 x_{1}-2 x_{2}, 3\left|x_{2}\right|\right)\) is not linear.

ANSWER:

Solution:

Step 1: Given that T() = (4 - 2, )

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