Scaling a row scales the determinant

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SUMMARY

The discussion focuses on the properties of determinants in linear algebra, specifically how scaling a row affects the determinant value. The key equation highlighted is Det(cA) = cDet(A), confirming that scaling a row by a constant c scales the determinant by the same factor. Additionally, it emphasizes that adding rows or columns does not alter the determinant, and the determinant of a transposed matrix remains unchanged (Det(AT) = Det A). The user struggles with applying these concepts to a specific matrix problem.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly determinants.
  • Familiarity with matrix operations, including row scaling and addition.
  • Knowledge of the properties of determinants, such as scaling and transposition.
  • Ability to interpret and manipulate mathematical equations.
NEXT STEPS
  • Study the properties of determinants in detail, focusing on scaling and addition.
  • Practice solving determinant problems using various matrix operations.
  • Learn about the implications of the determinant in linear transformations.
  • Explore the relationship between determinants and eigenvalues in linear algebra.
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Students of linear algebra, educators teaching matrix theory, and anyone looking to deepen their understanding of determinants and their properties in mathematical contexts.

Lifprasir
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Homework Statement


http://puu.sh/1rcsO

I got the first one from a simple scaling, but I can not figure out the second one.

Homework Equations


Det(cA) = cDet(A)
Scaling a row scales the determinant
Adding rows/columns to each other does not affect the determinant
Det(AT) = Det A

The Attempt at a Solution


So, shouldn't I be able to scale http://puu.sh/1rcyZ by -2, and just add row 2 and row 3 by multiples of row 1 ? I actually don't even think this is even close to right because the column 1 and 3 won't resemble each other at all once the row operations are done...
 
Last edited by a moderator:
Physics news on Phys.org
Hi Lifprasir! :smile:

Hint: what are the gaps between 1,2,3?

what are the gaps between -2,-8,-14? :wink:
 

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