*4. Determine whether each of the following functions is a linear transformation. If so, provide a proof; if not, explain why. X1 +2x2 X1 +2x2 а. Т b. T X2 X2
*4. Determine whether each of the following functions is a linear transformation. If so, provide a proof; if not, explain why. X1 +2x2 X1 +2x2 а. Т b. T X2 X2
*4. Determine whether each of the following functions is a linear transformation. If so, provide a proof; if not, explain why. X1 +2x2 X1 +2x2 а. Т b. T X2 X2
Transcribed Image Text:*4. Determine whether each of the following functions is a linear transformation. If so,
provide a proof; if not, explain why.
X1
X1 + 2x2
X1
X1 + 2x2
а. Т
b. T
=
X2
X2
2 Linear Transformations: An Introduction
101
X1 + 2x2
-C)-
X1
X1
с. Т
= x1 – X2
е. Т
X2
X2
X2
-X1 + 3x2
X1
|x2|
d. T
f. T: R" → R given by T (x) = ||x||
X2
3x1
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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