Question

Math

Posted 4 months ago

```
Select all linear transformations that are pirojoctions
A. $T(a, b, c)=(c, a, b)$
B. $T(a, b, c)=(c-b,-a, c)$
C. $T(a, b, c)=(-2 b, b,-a-2 b+c)$
D. $T(a, b, c)=(a, b, c)$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

To determine if $T(a, b, c) = (c - b, -a, c)$ is a projection, we check if $T(T(a, b, c)) = T(a, b, c)$. Calculating $T(T(a, b, c)) = T(c - b, -a, c) = (-a - (c - b), -c + b, c - b)$. Since $(-a - (c - b), -c + b, c - b) \neq (c - b, -a, c)$, it is not a projection

step 3

To determine if $T(a, b, c) = (-2b, b, -a - 2b + c)$ is a projection, we check if $T(T(a, b, c)) = T(a, b, c)$. Calculating $T(T(a, b, c)) = T(-2b, b, -a - 2b + c) = (b, -2b, -a - 2b + c)$. Since $(b, -2b, -a - 2b + c) \neq (-2b, b, -a - 2b + c)$, it is not a projection

step 4

To determine if $T(a, b, c) = (a, b, c)$ is a projection, we check if $T(T(a, b, c)) = T(a, b, c)$. Calculating $T(T(a, b, c)) = T(a, b, c) = (a, b, c)$. Since $(a, b, c) = (a, b, c)$, it is a projection

D

Key Concept

Projection

Explanation

A projection is a linear transformation $T$ such that $T(T(x)) = T(x)$ for all $x$.

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