Nemanjavuk69
Junior Member
- Joined
- Mar 23, 2022
- Messages
- 67
I have the following matrix
[math]\begin{matrix} 1 & 0 & -1\\ 2 & 3 & -1\\ 0 & 6 & 0 \end{matrix}[/math]
Following the text book linear algebra and its applications 6 global edition by David C. Lay on chapter 5.2 we can calculate the determinant by writing the characteristic equation like this
[math]\begin{matrix} 1-\lambda & 0 & -1\\ 2 & 3-\lambda & -1\\ 0 & 6 & -\lambda \end{matrix}[/math]
However, when doing the calculations I always end up with [imath]-\lambda^3+4\lambda^2-3\lambda-6[/imath] and that is not true, the actual equation should be [imath]-\lambda^3+4\lambda^2-9\lambda-6[/imath]
I am row expanding from the first column, so [math]a_{11}, a_{21}, a_{31}[/math]
I can therefor calculate the determinant as followed...
[math](1-\lambda) \cdot \begin{vmatrix} 3-\lambda & -1\\ 6 & -\lambda \end{vmatrix} -2 \cdot \begin{vmatrix} 0 & -1\\ 6 & -\lambda \end{vmatrix}[/math][math](1-\lambda) \cdot (3-\lambda) \cdot (-\lambda) + 6 - 2 \cdot 6[/math][math](1-\lambda) \cdot (-3\lambda+\lambda^2) + 6[/math][math]-3\lambda + \lambda^2 + 3\lambda^2 - \lambda^3 - 6[/math][math]-\lambda^3 + 4\lambda^2 - 3\lambda - 6[/math]
However, as stated before, the result is not right. Instead of [imath]-3\lambda[/imath] it should be [imath]-9\lambda[/imath]. Where am I doing something wrong? Any help is gladely appreciated.
[math]\begin{matrix} 1 & 0 & -1\\ 2 & 3 & -1\\ 0 & 6 & 0 \end{matrix}[/math]
Following the text book linear algebra and its applications 6 global edition by David C. Lay on chapter 5.2 we can calculate the determinant by writing the characteristic equation like this
[math]\begin{matrix} 1-\lambda & 0 & -1\\ 2 & 3-\lambda & -1\\ 0 & 6 & -\lambda \end{matrix}[/math]
However, when doing the calculations I always end up with [imath]-\lambda^3+4\lambda^2-3\lambda-6[/imath] and that is not true, the actual equation should be [imath]-\lambda^3+4\lambda^2-9\lambda-6[/imath]
I am row expanding from the first column, so [math]a_{11}, a_{21}, a_{31}[/math]
I can therefor calculate the determinant as followed...
[math](1-\lambda) \cdot \begin{vmatrix} 3-\lambda & -1\\ 6 & -\lambda \end{vmatrix} -2 \cdot \begin{vmatrix} 0 & -1\\ 6 & -\lambda \end{vmatrix}[/math][math](1-\lambda) \cdot (3-\lambda) \cdot (-\lambda) + 6 - 2 \cdot 6[/math][math](1-\lambda) \cdot (-3\lambda+\lambda^2) + 6[/math][math]-3\lambda + \lambda^2 + 3\lambda^2 - \lambda^3 - 6[/math][math]-\lambda^3 + 4\lambda^2 - 3\lambda - 6[/math]
However, as stated before, the result is not right. Instead of [imath]-3\lambda[/imath] it should be [imath]-9\lambda[/imath]. Where am I doing something wrong? Any help is gladely appreciated.