How Do You Solve for x Given the Determinant of a Matrix?

Click For Summary
SUMMARY

The discussion focuses on solving for the variable x in a matrix determinant equation. The determinant of the matrix |x-2 3| |x x+1| is calculated as x^2 - 4x - 2. To find the values of x that yield a determinant of 3, the equation x^2 - 4x - 2 = 3 must be solved, leading to the quadratic equation x^2 - 4x - 5 = 0.

PREREQUISITES
  • Understanding of matrix determinants
  • Familiarity with quadratic equations
  • Basic algebraic manipulation skills
  • Knowledge of solving polynomial equations
NEXT STEPS
  • Learn how to calculate determinants of larger matrices
  • Study the quadratic formula for solving equations
  • Explore applications of determinants in linear algebra
  • Investigate the properties of eigenvalues and eigenvectors
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as educators looking for examples of determinant calculations and polynomial solutions.

Nile3
Messages
42
Reaction score
0
Find the value of x when the matrix equals 3:

|x-2 3|
|x x+1|

so I find the determinant:
(x-2)(x+1)-(x)(3)
x^2-4x-2

How do I find which values are giving 3 from here?
 
Physics news on Phys.org
Nile3 said:
Find the value of x when the matrix equals 3:
You mean when the determinant of the matrix equals 3. The matrix doesn't equal 3.

You found
$$\begin{vmatrix} x-2 & 3 \\ x & x+1 \end{vmatrix} = x^2-4x-2$$ so set that expression equal to 3 and solve for x.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
10
Views
2K
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K