Linear Algebra Help: Struggling with Question 3 Part a)

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SUMMARY

The forum discussion centers around a user's struggle with Question 3 Part a) from a Linear Algebra lab assignment. The user is specifically confused about demonstrating a concept through algebraic calculation, particularly regarding dot products and matrix transposition. They question how the dot product of a matrix and its transposed version can yield an identity matrix, especially when dealing with orthogonal vectors. The discussion highlights the need for clarity in understanding matrix operations and their implications in linear algebra.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically dot products.
  • Familiarity with matrix operations, including transposition.
  • Knowledge of orthogonal vectors and their properties.
  • Basic proficiency in algebraic calculations related to matrices.
NEXT STEPS
  • Study the properties of dot products in the context of matrices.
  • Learn about the significance of the identity matrix in linear algebra.
  • Explore examples of orthogonal vectors and their representations in matrix form.
  • Review algebraic proofs involving matrix transposition and multiplication.
USEFUL FOR

Students of linear algebra, educators teaching matrix operations, and anyone seeking to deepen their understanding of dot products and orthogonality in vector spaces.

jtm
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I'm really really struggling on this question and am becoming very depressed from the stress that is being generated.

http://www.math.rutgers.edu/courses/250/250C-f05/f05lab6.pdf

Question 3 Part a) I've been stuck on it for hours. The last part where it talks about "show by algebraic calculation" Please help me. I'm really sad. :confused: :confused: :confused: :confused:
 
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I've tried using dot products but I don't see how I can represent that into a matrix. I don't see how doing a dot product of a matrix with a transposed matrix is even possible. Q dot product Q' is the identity matrix somehow.. wouldn't it be all 0s since the vectors are all orthogonal to each other?
 

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