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QUESTION 3 Let

`T:R^(3)->R^(3)`

defined by

`T([[x],[y],[z]])=[[x-y],[2z],[x+z]]`

. 3.1. Show that

`T`

is linear. 3.2. Find the translation matrix

`A`

of

`T`

. 3.3. Use the result in (3.2) to find

`T([[1],[-2],[2]])`

.