Let f : X → Y, A¡ C X for all i e I and B; C Y for all j e J where I and J are some nonempty index sets. Prove the following statements. (a) f (Uier Ai) = Uier f(A;); (b) ƒ (Niei Ai) C Nier S(A;); (c) f- (Njej B;) = Njess(B;). Why wouldn't a set equality hold for part (b)? Explain.

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.