How to Solve an Equation Involving a Determinant?

In summary, a determinant is a mathematical concept used to determine properties of a square matrix, such as invertibility and solutions to systems of linear equations. It is calculated using a specific formula and has significance in linear algebra, as it can determine invertibility and calculate area/volume. The determinant can be negative, indicating a negative orientation, and is related to the matrix's eigenvalues.
  • #1
rowdy3
33
0
Solve the following equation involving a determinant

det x (x+2)
9 2x = 0
I did x * 2x - 9(x+2)
It came out to 2x^2 - 9x - 18 = 0
Do I have to do anything else like a quadratic equation? I went to a math tutor and he wasn't sure. I scanned the problem and it's number 11.
http://pic20.picturetrail.com/VOL1370/5671323/23539305/392720959.jpg
 
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  • #2
No. You simply solve the quadratic and check your solutions within the original equation.
 

FAQ: How to Solve an Equation Involving a Determinant?

What is a determinant?

A determinant is a mathematical concept that is used to determine properties of a square matrix, such as its invertibility and the solution to a system of linear equations.

How is the determinant of a matrix calculated?

The determinant of a matrix is calculated by using a specific formula depending on the size of the matrix. For a 2x2 matrix, the determinant is calculated by multiplying the two main diagonal elements and subtracting the product of the other two elements. For larger matrices, the Laplace expansion method or the Gaussian elimination method can be used.

What is the significance of the determinant in linear algebra?

The determinant is an important tool in linear algebra as it can be used to determine if a matrix is invertible, which is crucial in solving systems of linear equations. It is also used to calculate the area and volume of a parallelogram or parallelepiped, respectively, formed by the column or row vectors of the matrix.

Can the determinant of a matrix be negative?

Yes, the determinant of a matrix can be negative. This indicates that the matrix has a negative orientation, meaning that the transformation it represents involves a reflection or a combination of reflections and rotations.

How is the determinant of a matrix related to its eigenvalues?

The determinant of a matrix is equal to the product of its eigenvalues. This means that the determinant can be used to determine the eigenvalues of a matrix and vice versa. Additionally, if a matrix has a determinant of 0, then at least one of its eigenvalues is also 0.

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