Question

What is the determinant of H= 0 2 3-1 3 56 3 -2

Answer 1

`-7`

1) Since this is a Matrix 3x3 we can make use of the Sarrus Rule to find the determinant of this Matrix:

`\begin{bmatrix}0 & 2 & 3 \\ -1 & 3 & 5 \\ 6 & 3 & -2 \\ \end{bmatrix}`

2) We can do that by copying two columns to the right of the Matrix, and multiplying the entries, this way:

Now, let's add algebraically each diagonal and subtract from the other like this:

`\begin{gathered} \det (H)=\lbrack60-9+0\rbrack-\lbrack54+4+0\rbrack \\ \det H)=51-58 \\ \det (H)=-7 \end{gathered}`