Mark each of the following statement true or false: The transformation defined b

DofotheroU

DofotheroU

Answered question

2021-10-21

Mark each of the following statement true or false: The transformation defined by T(x) = -x is a linear transformation.
T:R2R2

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-10-22Added 93 answers

Step 1
Given transformation is:
T:R2 Step 1 Given transformation is:
T:RR2 defined by T(x) = -x
We have to prove that T is a linear transformation.
Step 2
Let x, y belong to R and c be a scalar.
Then we get,
T(x + y) = -(x + y) = -x - y = (-x) + (-y) = T(x) + T(y)
T(cx) = -cx = c (-x) = c T(x)
Hence T becomes a linear transformation.

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