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 )
6. Determine if the linear transformation T(x1, x2, x3)
=
(2x1 — X2, —X1 − 2x2 + x3, x1 − 3x2 + x3) is
(a) one-to-one
(b) onto
Hint: use your answer from problem 4.
.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:
Chapter 6 Solutions
Differential Equations and Linear Algebra (4th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
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