Skip to main content
Calculate Determinant
Tick mark Image
Evaluate
Tick mark Image

Share

det(\left(\begin{matrix}0&1&1\\1&0&1\\1&1&2\end{matrix}\right))
Find the determinant of the matrix using the method of diagonals.
\left(\begin{matrix}0&1&1&0&1\\1&0&1&1&0\\1&1&2&1&1\end{matrix}\right)
Extend the original matrix by repeating the first two columns as the fourth and fifth columns.
1+1=2
Starting at the upper left entry, multiply down along the diagonals, and add the resulting products.
2=2
Starting at the lower left entry, multiply up along the diagonals, and add the resulting products.
2-2
Subtract the sum of the upward diagonal products from the sum of the downward diagonal products.
0
Subtract 2 from 2.
det(\left(\begin{matrix}0&1&1\\1&0&1\\1&1&2\end{matrix}\right))
Find the determinant of the matrix using the method of expansion by minors (also known as expansion by cofactors).
-det(\left(\begin{matrix}1&1\\1&2\end{matrix}\right))+det(\left(\begin{matrix}1&0\\1&1\end{matrix}\right))
To expand by minors, multiply each element of the first row by its minor, which is the determinant of the 2\times 2 matrix created by deleting the row and column containing that element, then multiply by the element's position sign.
-\left(2-1\right)+1
For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.
-1+1
Simplify.
0
Add the terms to obtain the final result.