Question Video: Finding the Determinant of a Matrix that Includes a Row of Zeros Mathematics

Find the value of |5, −1, −8 and 0, 2, 60 and 0, 0, 0|.

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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.

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