Finding the Determinant of A: Step-by-Step Guide

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SUMMARY

The discussion centers on calculating the determinant of a 2x2 matrix A, specifically A = \(\begin{bmatrix}1 & 2 \\ 2 & 3\end{bmatrix}\). The determinant is computed using the formula |A| = ad - bc, where a, b, c, and d are the elements of the matrix. For matrix A, the determinant is calculated as (1)(3) - (2)(2) = 3 - 4 = -1. This determinant value is essential for further calculations involving the adjugate matrix ADJ.A and the inverse of matrix A.

PREREQUISITES
  • Understanding of 2x2 matrix operations
  • Familiarity with determinant calculation formulas
  • Knowledge of adjugate and inverse matrix concepts
  • Basic algebra skills for matrix element manipulation
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  • Learn about calculating determinants for larger matrices, such as 3x3 matrices
  • Study the properties and applications of adjugate matrices
  • Explore the relationship between determinants and matrix invertibility
  • Investigate numerical methods for determinant calculation in computational tools
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Homework Statement



A= 1 2 CF.A= 3 -2 ADJ.A= 3 -2
2 3 -2 1 -2 1

Next i need to find determinant of A so then i can do ADJ.A / determinant.A

Homework Equations



How do i work out the determinant, is there a specific way and procedure as i am unsure.

The Attempt at a Solution

 
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You are saying, I believe, that
[tex]A= \begin{bmatrix}1 & 2 \\ 2 & 3\end{bmatrix}[/tex]
[tex]CF.A= 3 & -2 \\ -2 & 1\end{bmatrix}[/tex]
(which is [itex]-A^{-1}[/itex])
and
[tex]Adj A= \begin{bmatrix}3 & -2 \\ -2 & 1\end{bmatrix}[/tex]

In any case, if you are attempting to find a determinant, I am surprised that you do not know that
[tex]\left|\begin{array}{cc}a & b \\ c & d\end{array}\right|= ad- bc[/tex].
 

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