Video: Evaluating 3 × 3 Determinants

Find the value of |2 2 6, −3 1 −2, −5 −1 −4|.

01:24

Video Transcript

Find the value of the determinant of this three-by-three matrix.

So these lines are not absolute value lines; they mean we’re taking the determinant. And the way that we’ll do that is we will take two times the determinant of the numbers that are not in the row or column of that two and then subtract two times the determinant of the numbers that are not in the row or column of this two and then we add six times the determinant of the numbers that are not in the row or the column of the six.

So how do we take the determinant? How do we find it? Well, it’s kind of like cross-multiplying. We take 𝑎 times 𝑑 and then subtract 𝑏 times 𝑐. So we have two times one times negative four minus negative two times negative one minus two times negative three times negative four minus negative two times negative five plus six times negative three times negative one minus one times negative five.

So after multiplying the numbers inside the parentheses, we need to add the numbers now inside the parentheses. Now the very last set, the three minus negative five in the yellow, two negatives make a positive, so we have two times negative six minus two times two plus six times eight. So we have negative 12 minus four plus 48, which gives us an answer of 32.

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