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Academia.edu is a platform for academics to share research papers.A vector vectore (also called a linear vectore) is a collection of objects called vectors which may be added together and multiplied (scaled) by numbers called scalars. In mathematics and vector algebra the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional vectore (R 3) and is denoted by the symbol .

2.A history of Turnpikes. The turnpike theory is originated in two famous papers. One is the paper by John von Neumann (1937) vectorled A Model of General Economic Equilibrium and the other is the one by Frank Ramsey (1928) vectorled connect to download. Get pdf. Essential Mathematics for Economic vectorysis 4th editionDefinition 1 The determinant det A also denoted A of an n n square matrix A is defined recursively as follows If A is a 1 1 matrix [a] (i.e. a scalar) then det A a. Otherwise where A ij is matrix A with row i and column j removed. Note that if A then we use the notation