PROFESSOR: Use determinant notation to find a cross b, where a is the vector 8, 2, 3, and b is the vector negative 1, 0, 4. Using determinant notation, a cross b is equal to the determinant of the matrix i, j, k as our first row, 8, 2, 3 as our second row, and negative 1, 0, 4 in our third row. Now we get to go back to minor matrices here.

So the first determinant I'm going to find is going to neglect the i, or the first column. I'm going to have a little minor matrix that is 2, 3, 0, 4 multiply i minus-- if I eliminate the j column, this all the matrix 8, 3, negative 1, 4, that matrix, multiply by j. Plus for the k value, I'll eliminate the k column and the matrix 8, 2, negative 1, 0, k,

Now find the determinant of each of these. Remember, that's ad minus bc. So 2 times 4 is 8 minus 3 times 0, which is 0, i. So 8 minus 0 i. Next, I'll have minus 8 times 4, which is 32, minus 3 times negative 1. That's negative 3. So 32 minus negative 3 j.

And then finally, plus 8 times 0, which is 0, minus 2 times negative 1, so negative 2. So I have 0 minus negative 2 k. So this results in 8i minus 35j plus 2k. And that is a cross b.