Video: Evaluating a 2 × 2 Determinant

Alex Cutbill

Find the value of the determinant of the matrix −2, −9, 7, 7.

01:28

Video Transcript

Find the value of the determinant of the matrix negative two, negative nine, seven, seven.

The fact that we have vertical bars here and not square brackets tells us this is a determinant. The determinant of a general two-by-two matrix with entries 𝑎, 𝑏, 𝑐, and 𝑑 is written just like the matrix, but instead of having square brackets on either side, we have vertical bars as mentioned before, and the value of this determinant is 𝑎𝑑 minus 𝑏𝑐.

So let’s use this definition to evaluate the determinant that we have, the determinant of negative two, negative nine, seven, seven. We take a look at the formula. The first term 𝑎𝑑 is the product of the entries on the leading diagonal of the matrix. In our case, that’s negative two times seven. And from that, we have to subtract the product of the other two entries 𝑏 times 𝑐 in our formula, which is negative nine times seven.

And now we just need to evaluate this. We could do this by calculator straight away or by hand, evaluating each term to get negative 14 minus negative 63, which is 49. So the determinant of the matrix negative two, negative nine, seven, seven is 49.

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