1. Home
  2. Calculators
  3. Calculators: Linear Algebra
  4. Linear Algebra Calculator

Determinant of $$$\left[\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right]$$$

The calculator will find the determinant of the square $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right]$$$, with steps shown.

Related calculator: Cofactor Matrix Calculator

A

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Calculate $$$\left|\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right|$$$.

Solution

The determinant of a 2x2 matrix is $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right| = \left(8 - \lambda\right)\cdot \left(8 - \lambda\right) - \left(8\right)\cdot \left(8\right) = \lambda^{2} - 16 \lambda$$$

Answer

$$$\left|\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right| = \lambda \left(\lambda - 16\right)$$$A