Ch7Pr26a: Kernel and Nullity of a 4x3 matrix

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How to find the kernel and nullity of a 4x3 linear transformation. This is Chapter 7 Problem 26a of the MATH1231/1241 Algebra Notes, presented by Norman Wildberger of UNSW.
  1. MathsStatsUNSW
  2. Mathematics
  3. UNSW
  4. Kernel
  5. Rank–nullity Theorem
  6. Matrix (Literature Subject)
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Комментарии
Автор

Prof Wildberger you are a fantastic teacher. Praying Tanaka has a final very soon and was struggling with this topic, but your conceptual explanation and the example were really helpful. Praying Tanaka hopes to dig through your lectures and find one on orthogonality too- another topic that didn't really click.

nataliatothemoon
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what's the name of the song in the beginning please. Quite delightful.

enyioma
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he is really a teacher and his experiences speaks aloud

FreedomForKashmir
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sir this is a 3x4 matrix. how do u determine the dimension is it based on the column or rows

hariharannair
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So the reason the nullity/dimension of the kernal is ONE (and the subspace is a line) is the occurence of THREE pivot columns in RREF, leaving a SINGLE parameter.

abajabbajew
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Thank you so much, this was so clear and informative!.

AbooddHamdan
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Thankyou so much❤🎉well explained and clear understandable

micahteiul
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Why is it R^4 at 0:50 ? The dimension of the environment isn't given by the lines of the matrix (which represent the coordinates of the vector)? The columns represent the no of vectors, not the coordinates which give the environment's dimension

psawyer
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Thank you sir for the clear explanation.

dragonz_breath
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you have a mistake on the 0's columns 0, 0, 1 is 0, 0, 0

jmzefren
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Looks like it's -1/3 R2 for a new R2.

rcfoley