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Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
Choose and fix, in order, two columns of A, called the indexing columns. Because the strength is 2 and the index is 1, all ordered pairs (i, j) with 1 ≤ i, j ≤ n appear exactly once in the rows of the indexing columns. Here i and j will in turn index the rows and columns of a n×n square.
In other words, the two variables are not independent. If there is no contingency, it is said that the two variables are independent. The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used.
The column space of a matrix A is the set of all linear combinations of the columns in A. If A = [a 1 ⋯ a n], then colsp(A) = span({a 1, ..., a n}). Given a matrix A, the action of the matrix A on a vector x returns a linear combination of the columns of A with the coordinates of x as coefficients; that is, the columns of the matrix generate ...
combinationsfor Microsoft Word, LibreOffice, OpenOffice.org (from 3.0) Key combination in other word processors Windows Alt Key Codes [5] Unicode name Unicode code Unicode code Space · Space: SPACE 0x20 0032 Non-breaking space ° Ctrl+⇧ Shift+Space: Ctrl+Space for FrameMaker, LyX (non-Mac), OpenOffice.org (before 3.0), WordPerfect
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Moreover, this amounts to forming a linear combination of the columns of A that effectively involves only finitely many of them, whence the result has only finitely many nonzero entries because each of those columns does. Products of two matrices of the given type are well defined (provided that the column-index and row-index sets match), are ...
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