Why do you put the number 1, instead of any other number, in a column or row when finding the determinant of a matrix in order to find the area of a triangle?
2026-04-07 22:59:22.1775602762
1's in the last column for a matrix to find an area of triangle using the determinant of a matrix
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The determinant of a $3\times3$ matrix is equal (in absolute value) to the volume of the paralellepiped with sides defined by the vectors that are the rows of that matrix, and the volume of the tetrahedron with those vectors as its slant edges is half that. If you place your triangle on the plane $z=1$ in $\mathbb R^3$ by setting all of the $z$-coordinates to $1$, together with the origin you get a tetrahedron with volume equal to $1$ (the height) times the area of the triangle.