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. 0.5 7 50.5 3 90.5 1 3

Accepted Answer

Hey everyone here we are asked to use diagonals to evaluate the following third order determinant Now to begin using diagonals. We want to first copy down these first three columns and repeat these first two given columns. So for our first column we have 615. Then we have 82 four for the second column. And for our third column we have 0.10 point 10.1. And now we want to repeat the first two columns. So our fourth column will be 615, and then our fifth column will be 8 to 4. And now we just want to begin drawing in our diagonals. So for the first three columns will be going from left to right. And for our last three columns, the diagonals will go from right to left. So starting with left to right, we go from six through 2 to 0.1. We then go from 8 to 0.125. And then lastly we go from 0.1 to 1 to four and now going from right to left, beginning with the right most column, we go from 8 to 1 to 0.1. We then go from 6 to 0.1 to four. And lastly we go from 0.1 to 2 to five. And now we just want to take the product of the diagonals, the numbers within the diagonal. So beginning with our right to left diagonals, we have 0.1 times two times five which gives us one, we then have six times 0.1 times four giving us 2.4. And then we have eight times one times 0.1 giving us 0.8. And now for our diagonals which go from left to right, we have six times two times 0.1 which is 1.2. We then have eight times 0.1 times five which is four. And lastly we have 0.1 times one times four, giving us 0.4. And now to actually start fighting the determinant, we want to add the products with diagonals that go from left to right and subtract the products which have diagonals that go from right to left. So starting with our positive terms going from left to right, we have 1.2 plus four plus 0.4 and now Going from right to left we have - -2.4 -0.8. And so for our green products here, the diagonals from left to right, we have a total of 5.6 and then we have minus the right to left diagonals which come to 4.2. And now subtracting these terms, we find our determinant which is just 1.4 which is answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time

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In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 0.5 7 50.5 3 90.5 1 3

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