Linear algebra adjoint, determinant

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SUMMARY

The discussion focuses on calculating the (2,3) entry of the inverse of matrix A, defined as A=[1 2 1; 0 4 3; 1 2 2]. Participants confirm that to find this entry, one must compute the quotient of the (2,3) entry of the adjugate matrix adj(A) and the determinant det(A). The confusion regarding whether to compute the entire inverse A^(-1) is clarified, emphasizing that only the specific entry is required.

PREREQUISITES
  • Understanding of matrix operations, specifically matrix inversion
  • Knowledge of determinants and adjugate matrices
  • Familiarity with the properties of linear algebra
  • Ability to compute specific entries of matrices
NEXT STEPS
  • Learn how to compute the determinant of a 3x3 matrix
  • Study the properties and computation of the adjugate matrix
  • Explore the relationship between adjugate matrices and matrix inverses
  • Practice finding specific entries of matrix inverses using determinants
USEFUL FOR

Students studying linear algebra, particularly those focusing on matrix theory and inverses, as well as educators looking for examples of determinant and adjugate matrix applications.

Mdhiggenz
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Homework Statement



Given A=[1 2 1; 0 4 3; 1 2 2]
determine the (2,3) entry of A-1 by computing a quotient of two determinants.

This problem confused me a bit, do they just want us to divide the adj(A) by the det(A) in order which would give us A-1 and just state the (2,3) entry from there?

Thanks

Higgenz



Homework Equations





The Attempt at a Solution

 
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Mdhiggenz said:

Homework Statement



Given A=[1 2 1; 0 4 3; 1 2 2]
determine the (2,3) entry of A-1 by computing a quotient of two determinants.

This problem confused me a bit, do they just want us to divide the adj(A) by the det(A) in order which would give us A-1 and just state the (2,3) entry from there?

Thanks

Higgenz

Homework Equations


The Attempt at a Solution


You don't need to compute the whole A^(-1). But as you say, they just want you to compute adj(A)(2,3)/det(A). Just the one entry of A^(-1).
 

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