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Since there is a 2 is in the second row and third column the sign will be negative (-1)^(3+2) = (-1)^5 = -1. Here is the sign chart (same one that is used in the video): tinyurl.com/cofactorsigns

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Given that the initial value is (1,4) then x = 1 and y = 4.

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"Linear Algebra and Its Applications" by David Lay, 6th edition.

The answer is 6, I would suggest reviewing your work and checking your co-factor signs. matrixcalc.org/det.html#%7B%7B4,0,-7,3,-5%7D,%7B0,0,2,0,0%7D,%7B7,3,-6,4,-8%7D,%7B5,0,5,2,-3%7D,%7B0,0,9,-1,2%7D%7Dexpand-along-column1

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The sign of the cofactor is (-1)^(i +j), so since 2 is located in the second row (i = 2) and third column (j = 3) then the sign will be (-1)^(2 + 3) = (-1)^5 = -1. Here is the sign chart (same one that is used in the video): tinyurl.com/cofactorsigns

Yes, but keep in mind that certain elementary row operations will change the determinant of the original matrix. This is discussed in my notes: blogs.nvcc.edu/mwesterhoff/files/2019/09/Section3.2-Properties-of-Determinants.pdf

I believe videos can be helpful, but reading and understanding material from a book forces the mind to engage more deeply, resulting in better retention. When I was in college, we didn't have videos, so we had to thoroughly read the material. If we didn't understand something, we would re-read it or look for alternative explanations in other textbooks, often spending a lot of time in the library. Otherwise, we had to visit the professor during office hours, hoping they could provide a hint, as they definitely wouldn't solve it for us. Struggling with a problem or concept is a crucial part of learning math. That's why I always tell my students to try to solve the problem before looking at the detailed solution. It's fine if they don't get it right on the first attempt; they just need to review their work, think about it, and try again.

​@@DoctrinaMathVideos Yep, looking at online lectures is a last resort. I said that I should do it more often because sometimes I am stubborn about that to a fault and don't use anything other than what the course gives to me for far too long.

I am pleased you are intrigued by this. Feel free to share which particular subjects you would like me to cover in my videos.

It is great to hear from you! I am glad you are enjoying the new video uploads. Let me know if there are any topics you would like to see covered in future videos.

I am glad that you found this lecture to be helpful.

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Hello. "Linear Algebra and Its Applications", 5th edition, David Lay. Problem #33 of Section 1.1 on page 11.

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Just apply the co-factor expansion to each of the other columns that do not contain zero.

I think you will have to add additional terms and include non zero row or column values

This example was specifically chosen (by request) to illustrate that it is important to look at the rows and columns carefully to illustrate that the number of steps can be reduced by choosing the row or column with the most zeros. Once you learn the basic technique of the cofactor expansion concept it becomes an iterative process. If an application requires the use of the determinant of a 4 x 4 matrix or higher then I would highly recommend using some type of computational tool such as Matlab or Octave.

@@DoctrinaMathVideos Tell that to my linear algebra professor who expects us to do the determinant of a 5x5 by hand without a calculator! 😭😭

Been there done that, but I do find it kind of ridiculous. Better hope that there is a column or row with some zeros in it. :)

It's not really trick it's more of just taking advantage of the row or column with the most zeros and understanding how the cofactor technique works for finding the determinant of a matrix.

Good luck!

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Glad this was helpful. This function shown in the video does not have an antiderivative so you must rely on technology (such as the graphing calculator) or numerical techniques such as the Trapezoidal rule, Simpson's rule, and series.The choice of numerical method depends on the nature of the function being integrated, the desired level of accuracy, and the computational resources available. In more advanced math/engineering courses and scientific applications, you will often encounter a combination of these techniques to solve complex integration problems effectively.

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There is no limitation for the cofactor expansion technique as long as the matrix is square. The last step where you see the diagonal lines can only be applied for 3 x 3 matrices. Instead of the diagonal lines approach you could have continued using the cofactor approach and end up with the same solution.

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