Use the determinant theorems to evaluate each determinant. See Ex...

Question

Use the determinant theorems to evaluate each determinant. See Example 4.

Accepted Answer

Hello, today we're gonna be taking the determinant using the determinant theorems. So we're given a three by three matrix and the three by three matrix has the elements three negative 6487, 12, 5, 13 and eight. Now, in order to get the determinant, there's a bit of simplification that we can do to the current matrix. The first thing we can do is we can simplify the second row. We can allow the second row or simplify it by multiplying the third row by negative one and adding those values to the second row in order to do this, we're gonna write down the 1st and 3rd row since these values are not being changed. So we're going to have three negative 64, 5, 13 and eight. Now keep in mind we're multiplying the values of row three by negative one and adding them to row two. So five times negative one is going to give us negative five and eight minus five is going to give us three negative thir I'm sorry, 13 times negative one is going to give us negative 13 and seven minus 13 is going to give us negative six and eight times negative one is going to give us negative eight and minus eight is going to give us four. So what we have is a new three by three matrix where the 1st and 2nd row are identical to each other. Now, using the determinant theorems, one of the theorem states that if you have any rows inside your matrix that are identical to each other, then the determinant is automatically going to be assigned to zero here. Since the elements in the 1st and 2nd row are exactly the same to each other, that tells us that the determinant of this matrix is going to equal to zero. And that is going to be the determinant to this problem. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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Use the determinant theorems to evaluate each determinant. See Example 4.

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