Let be the matrix whose entries are all ones, except for zeros directly below the main diagonal; for example,
Find the determinant of .
Therefore, the determinant of the given matrix is given by,
A determinant is a unique number associated with a square matrix.
A determinant is a scalar value that is a function of the entries of a square matrix.
It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.
Using the Laplace expansion along the row, we see that the first addends are 0, because the corresponding minors for the first 2 elements are 0, since each of them has columns with all entries 1; and the entry in row and column is 0.
Thus, we're only left with . Since , we have .
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