Video Transcript
Find the value of the determinant
of the three-by-three matrix five, negative one, negative eight, zero, two, 60,
zero, zero, zero.
In this question, we’re asked to
evaluate the determinant of a given three-by-three matrix. We could do this by using the
definition of a determinant. However, there’s actually an easier
method if we can just notice the property of this matrix. We need to notice that this is an
upper triangular matrix. This means every entry below the
leading diagonal of this matrix is equal to zero. The leading diagonal of a matrix is
the entries whose row number is equal to the column number. So, for this matrix, that’s five,
two, and zero. So, this matrix is an upper
triangular matrix.
And we recall the determinant of
any square triangular matrix is the product of all of the entries on its leading
diagonal. In our case, the leading diagonal
has terms five, two, and zero. Therefore, the determinant of this
matrix is five multiplied by two multiplied by zero, which we can evaluate is equal
to zero.
Therefore, the determinants of the
three-by-three matrix five, negative one, negative eight, zero, two, 60, zero, zero,
zero is equal to zero.
