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and W be two vector spaces with zeros respectively 0, and 0. Let T: VW be defined by T (v) VvE V. Let Ker (T) denote the kernel of T and Ran (T) the range of T. Which one of the owing gives the correct information about the kernel and range of T ? Ler (T) = V en WT W. Jone of the other options. Ker (T) = (Ov) and Ran (T) = (0) - Ker (T) = W en W₁ = (Ow). / Ker (T) = V and Ran (T) = (On). Ker (T) = (0y) and Ran (T) = W. Ker (T) = (0) and Ran (T) = V.

and W be two vector spaces with zeros respectively 0, and 0. Let T: VW be defined by T (v) VvE V. Let Ker (T) denote the kernel of T and Ran (T) the range of T. Which one of the owing gives the correct information about the kernel and range of T ? Ler (T) = V en WT W. Jone of the other options. Ker (T) = (Ov) and Ran (T) = (0) - Ker (T) = W en W₁ = (Ow). / Ker (T) = V and Ran (T) = (On). Ker (T) = (0y) and Ran (T) = W. Ker (T) = (0) and Ran (T) = V.

Advanced Engineering Mathematics
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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Let V and W be two vector spaces with zeros respectively 0, and 0. Let T: VW be defined by T (V) = V. Let Ker (T) denote the kernel of T and Ran (T) the range of T. Which one of the following gives the correct information about the kernel and range of T ? A. Ker (T) = V en WT = W.. B. None of the other options. OC. Ker (T) = (0y) and Ran (T) = (0). OD. Ker (T) = W en WT = (Ow). / E. Ker (T) = V and Ran (T) OF. Ker (T) = {0y) and Ran (T) = W. G. Ker (T) = (0) and Ran (T) = v. (On
Transcribed Image Text:Let V and W be two vector spaces with zeros respectively 0, and 0. Let T: VW be defined by T (V) = V. Let Ker (T) denote the kernel of T and Ran (T) the range of T. Which one of the following gives the correct information about the kernel and range of T ? A. Ker (T) = V en WT = W.. B. None of the other options. OC. Ker (T) = (0y) and Ran (T) = (0). OD. Ker (T) = W en WT = (Ow). / E. Ker (T) = V and Ran (T) OF. Ker (T) = {0y) and Ran (T) = W. G. Ker (T) = (0) and Ran (T) = v. (On
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