Video: Adding Determinants of Matrices

Find the value of the determinant of the matrix 8, −2, 6, −9 + the determinant of the matrix 3, −11, −15, 6.

02:17

Video Transcript

Find the value of the determinant of the matrix eight, negative two, six, negative nine plus the determinant of the matrix three, negative 11, negative 15, six.

The first thing we can see is that both of our matrices are two by two. And actually, to find the determinant of a two-by-two matrix, we have a particular rule. And this rule tells us that the determinant of a two-by-two matrix in the form 𝑎𝑏𝑐𝑑 is equal to 𝑎 multiplied by 𝑑 minus 𝑏 multiplied by 𝑐.

Okay, great! So now we have this rule. We can actually use it to help us solve the problem we have. So now we have our sum. And what we need to do is actually work out the value of each determinant and then add them together.

So first of all, we’re gonna have eight multiplied by negative nine. And that’s because that’s like our 𝑎 and our 𝑑. And then this is gonna be minus. Then we’ve got negative two multiplied by six. And that’s because this is our 𝑏 and our 𝑐 in our determinant. Okay, great! So that’s our first determinant taken care of.

Now let’s have a look at the second determinant. Well, we’re gonna be dealing with three multiplied by six because again this is our 𝑎 and our 𝑑. And then we’re gonna subtract negative 11 multiplied by negative 15. This is because this is our 𝑏 and our 𝑐.

Okay, great! So now we’ve got both our determinants. What we need to do is actually figure out what the value of each of them is. Okay, so our first determinant is gonna be equal to negative 72 plus 12. And then this is gonna be added to our second determinant, which is 18 minus 165, which is gonna be equal to negative 60 plus negative 147.

So therefore, it’s gonna be the same as negative 60 minus 147, which gives us an answer of negative 207. So therefore, we can say that the value of the determinant of the matrix eight, negative two, six, negative nine plus the determinant of the matrix three, negative 11, negative 15, six is gonna be equal to negative 207.

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