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@@WrathofMath I'll admit, I felt a bit of dramatic tension as you were doing the determinant calculation. At first, I thought the second time around hadn't added up to 51 as expected. But then I saw it did. Phew!
Makes a lot more sense than how my text book explained it. Not totally related to this video but linear algebra didn't start making sense to me until we got to the theory of linear algebra, Ax*=b & Ax0=0. That, in combination with understanding the column of A are vectors that form sub-spaces (especially when graphically displayed), made everything else fall into place. I wish more courses started there. It might seem like a mess at first, but it comes into focus. The other way just seems like a bunch of unrelated nonsense with no context, then at the end they tell you what for. Maybe I'm just different though.
That had to do with when he was talking about (-1)^i+j. The positions within the matrix are denoted by the a-subscript i,j system, where i references the row number and j references the column number. In a1,1 (the first position of the matrix) , i + j or 1+1 = 2. We take this 2 and put it to the exponent of (-1). (-1) squared is just positive 1. Therefore, the first position in the matrix has a positive cofactor. For the second position of the matrix, a1,2, 1 + 2 = 3. (-1)^3 is still negative 1, hence the second position in the matrix is negative. This pattern continues throughout the matrix.
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The definition was intractable and yet your patient exposition made it clear finally. Thanks!
Thank you! When I was recording this I kept screwing up a certain computation, ended up taking 40 minutes to record, glad it is done haha!
@@WrathofMath I'll admit, I felt a bit of dramatic tension as you were doing the determinant calculation. At first, I thought the second time around hadn't added up to 51 as expected. But then I saw it did. Phew!
Makes a lot more sense than how my text book explained it.
Not totally related to this video but linear algebra didn't start making sense to me until we got to the theory of linear algebra, Ax*=b & Ax0=0. That, in combination with understanding the column of A are vectors that form sub-spaces (especially when graphically displayed), made everything else fall into place. I wish more courses started there. It might seem like a mess at first, but it comes into focus. The other way just seems like a bunch of unrelated nonsense with no context, then at the end they tell you what for. Maybe I'm just different though.
I'd heard of cofactors before, but either forgot or never learned it was also named after Laplace!
Can you please make a video
Why there are alternate plus and minus sing in finding determinant..
That had to do with when he was talking about (-1)^i+j. The positions within the matrix are denoted by the a-subscript i,j system, where i references the row number and j references the column number. In a1,1 (the first position of the matrix) , i + j or 1+1 = 2. We take this 2 and put it to the exponent of (-1). (-1) squared is just positive 1. Therefore, the first position in the matrix has a positive cofactor. For the second position of the matrix, a1,2, 1 + 2 = 3. (-1)^3 is still negative 1, hence the second position in the matrix is negative. This pattern continues throughout the matrix.