Let V and W be vector spaces. The function is a linear transformation of V into W when the two properties below are true for all u and v in V and for any scalar c.
Assume the two vectors
The sum of the two vectors is,
Apply transformation on both side of the above equation.
The sum of the two transformations is,
From equation (1) and equation (2),
From the above result, the function is not a linear transformation.
Therefore, the statement is false.
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