For problems 1-8, verify directly from Definition 6.1.3 that the given mapping is a linear transformation. T : ℝ 2 → ℝ 2 defined by T ( x 1 , x 2 ) = ( x 1 + 2 x 2 , 2 x 1 − x 2 )
For problems 1-8, verify directly from Definition 6.1.3 that the given mapping is a linear transformation. T : ℝ 2 → ℝ 2 defined by T ( x 1 , x 2 ) = ( x 1 + 2 x 2 , 2 x 1 − x 2 )
.Define f: R- R by f(x) = rx + d, where r and d are real constants. Show that for f to be linear, it
is required that d 0. (the definition of a linear transformation is given in text section 1.8)
()-
4r1-2
. Is the transformation T
linear? YES or NO (circle one)
I2
X122+3
Justify your answer:
Show that the transformation :R2 → R3 defined by
T x
X1
X2
=
X1+X2
3X2
X1-X2
is linear by showing it satisfies the two properties given in the definition of a linear transformation.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY