i didn't quite understand how we applied the summation to elements a11, a21 & a31 pls help
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Academic discussion and doubt solving for: Logarithms, Set Theory, Matrices & Determinants, Permutation & Combination, Probability, Binomial Theorem
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what exactly do you not understand about it?
I'll answer regardless. If you have a doubt, ask away.
Here D1, D2 ... D5 is nothing but 5 different matrices will x = 1, 2 ... 5. Here column 2 and column 3 are the same. The difference in determinant will come from values of column 1. If you write 5 different determinants, only the values of column 1 will be different. There's a property which states that you can add (or separate) determinants if there is addition or subtraction between two variables and/or constants. Check the image I've uploaded. In that image column 2 and 3 are same, only column 1 is different. Thus, you can add column 1 of all 5 determinants which is nothing but the summation of x, x^2 and x^3 and solve the determinant. For example, the a11 of the 5 determinants would be 1,2,3,4,5 which will give a sum of 15. Similarly for a21 and a31.
I hope zyada complicated nahi kara hai maine.
this is EXACTLY what i had a heard time understanding. thank you so much!