Suppose that T: R2 --> R2 is a linear transformation such that T (i) = (1,2) and T (j) =(2,4_ . Show that T is not onto by finding one vector in the codomain that is not the image of any vector in the domain. Is T one-to-one? HW4.1. Suppose that T: R² →R² is a linear transformation such that T(i)=(1,2) andT(7)=(2,4). Show that T is not onto by finding one vethe image of any vector in the domain. Is T one-to-one?vector in the codomain that is not

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W4.1. Suppose that T: R² →R² is a linear transformation such that 1′(i)=(1,2) and (7)=(2,4). Show that I is not onto by finding one vector in the codomain that is not Le image of any vector in the domain. Is T one-to-one?

W4.1. Suppose that T: R² →R² is a linear transformation such that 1′(i)=(1,2) and (7)=(2,4). Show that I is not onto by finding one vector in the codomain that is not Le image of any vector in the domain. Is T one-to-one?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose that T: R2 --> R2 is a linear transformation such that T (i) = (1,2) and T (j) =(2,4_ . Show that T is not onto by finding one vector in the codomain that is not the image of any vector in the domain. Is T one-to-one?

HW4.1. Suppose that T: R² →R² is a linear transformation such that T(i)=(1,2) and
T(7)=(2,4). Show that T is not onto by finding one ve
the image of any vector in the domain. Is T one-to-one?
vector in the codomain that is not

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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