The calculation of the product of terms ##\prod_{j \neq i}^{6} (\lambda_{i}-\lambda_{j})## and ##\prod_{j \neq i}^{6} \frac{\lambda_{i}}{\lambda_{i}-\lambda_{j}}## involves evaluating all valid pairs (i, j) where i and j range from 1 to 6, excluding cases where i equals j. There are a total of 36 pairs, but only those where j is not equal to i contribute to the product. This results in 30 valid factors in the product, as each i has 5 corresponding j values.
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We require you to at least show your thoughts. To help you get started, there are 36 different pairs (i , j) pairs where i and j range between 1 and 6. Some of these pairs aren't going to be allowed in the product above. So how many factors will there be in the product?crv357 said:##\prod_{j \neq i}^{6} \frac{\lambda_{i}}{\lambda_{i}-\lambda_{j}}##