Give the ranks of both the matrix of coefficients and the augmented

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The discussion centers on determining the ranks of both the coefficient matrix and the augmented matrix in a linear algebra context. The user concludes that the rank of the augmented matrix is 1, which implies that the rank of the coefficient matrix is also 1. The user also explores methods for solving vector equations and finding distances between planes, indicating uncertainty in these areas. The conversation highlights the importance of understanding vector equations and matrix ranks for solving linear systems.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically matrix rank
  • Familiarity with vector equations and their representations
  • Knowledge of augmented matrices and their significance in linear systems
  • Basic skills in solving for variables in vector forms
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  • Study the properties of matrix rank and its implications in linear algebra
  • Learn how to derive and manipulate vector equations
  • Research methods for calculating distances between planes in three-dimensional space
  • Explore the relationship between coefficient matrices and augmented matrices in linear systems
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Students preparing for exams in linear algebra, educators teaching matrix theory, and anyone seeking to deepen their understanding of vector equations and matrix ranks.

salman213
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Hey!
I was looking at some problems since I have a mid term tomorrow and don't get how to do this one perhaps someone can help!


http://img143.imageshack.us/img143/3452/16856739ys6.jpg


I don't know if I am doing this right but i went backwards and found the vector equation to look like

x = 1 + 3t - s
y = s
z = t

(x,y,z) = (1,0,0) + t(3,0,1) + s(-1,1,0)
[1 1 3 l 1]
[0 0 0 l 0]
[0 0 0 l 0]


do the rank of the augmented matrix is 1 and does that mean the rank of the coefficient matrix is also 1 ?

b) for b part should i just plug in that coordinate in the x,y,z vecotr form to solve for s, and t and hope for the same answer to show it is a solution

c) for c should i use the two vectors given from the vector equation s(-1,1,0) and t(3,0,1)

d) not sure how to find distance between two planes :S


CAN SOMEONE TELL ME IF IM COMPLETELY LOST?
and cross them to get the normal then use the point given to get the scalar equation
 

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ok you can delete this thread now, my midterm already happened so its kinda useless now..lol thanks anyways
 

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