In Exercises 31–36, use the alternative method for evaluating thi...

Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 1 5 6 1 4 5 1 9 10

Third-order determinant matrix for Exercise 33 in college algebra, chapter on systems of equations.

Accepted Answer

Hey everyone here we are asked to use diagonals to evaluate the third order determinant. So we want to begin by copying down these three given columns and repeating the 1st and 2nd column. So our first column is 12 46. Our second column is 315. Our third column is 2 to 2 and now repeating the 1st and 2nd column. Our Fourth column is 1246 and our fifth column is 315. And now we can begin drawing in our diagonals. So for the first three columns we will be going from left to right and for our last three columns we will be going from right to left. So starting with our first column going from left to right, we go from 12 to 1-2. We then go from 3 to 2 to six and then we go from 2 to 4 to five and now going from right to left, starting at the right most column. We go from 3 to 4 to two, then we move to 12 which goes to two and then 25. And lastly we go from two to 126. And now we just need to take the product of each of the terms within the diagonal. So starting with this diagonal that ends at the first column. Here we have two times one times six which gives us 12. Moving on we have 12 times two times five which is 120. We then have three times four times two which is 24 and now moving on to the diagonals going from left to right. We have 12 times one times two which is 24 we then have three times two times six which is 36. And lastly we have two times four times five which is 40. And now to start finding the determinant we want to add the products with diagonals going from left to right and subtract the products with diagonals going from right to left, so starting with the diagonals from left to right. We have 24 plus 36 plus 40. And now with the diagonals going from right to left we have minus 12 mine -120 and -24. So simplifying, we see that our diagonals from left to right some to 100 and then we have minus our diagonals from right to left which is 156. And now just solving this we see that our determinant is negative 56 which is answer choice. C Thanks for watching. I hope you found this video helpful and I'll see you again next time

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 1 5 6 1 4 5 1 9 10

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