3. The vector space V over R has a basis {u, v, w}. The linear map ø : V → R² has the property thatdu) = (1): 0) = (); ocw) =2O(u) =Describe the kernel and image of ø, compute the dimensions of these and verify that the rank-nullitytheorem holds.

First we find the image and kernel. Then verify the rank nullity theorem.

3. The vector space V over R has a basis {u, v, w}. The linear map ø :V → R? has the property that du) = (:): 2 ; ø(w) = (;). Describe the kernel and image of ø, compute the dimensions of these and verify that the rank-nullity theorem holds.

3. The vector space V over R has a basis {u, v, w}. The linear map ø :V → R? has the property that du) = (:): 2 ; ø(w) = (;). Describe the kernel and image of ø, compute the dimensions of these and verify that the rank-nullity theorem holds.

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

3. The vector space V over R has a basis {u, v, w}. The linear map ø : V → R² has the property that
du) = (1
): 0) = (); ocw) =
2
O(u) =
Describe the kernel and image of ø, compute the dimensions of these and verify that the rank-nullity
theorem holds.

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