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Prior to the publication of this book, many organisations at that time had little guidance on how to plan and make decisions for the future; many still relied on conventional forms of planning that involved decisions based on an extended budgeting system which in turn is derived on a projected budgetary outcome to some point in the future (Chartered Institute of Management, 2003).

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Also given were matrices A and B, defined as aX and bY, respectively. Note that a and b are constants. First, recall that when multiplying constants to any matrix, we simply multiply the constant with every element of the matrix. To illustrate:

Once again, the general expression is shown valid. It is also important to note that this general statement will only yield results for values of n>0. Matrices can not be raised to negative exponents.

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This trend forces business organizations to rethink their strategies in order to compete more efficiently and more profitably. On the other hand, these developments in the market also present opportunities for business organizations especially in the way they market their products and services to their specific target markets. In order to choose the strategic path that a company should take, it should first identify the strategic marketing options available for it (Kotler 2002).

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In particular, these two matrices commute. Then we can apply Newton's formula (see [2], this formula is usually proved for real numbers, but it holds more generally for square, commuting1, matrices; the proof is the same) to compute the powers of K. The formula is:

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For example, with the power of vision a person can perceive height and width of three dimensional objects with ease but would have trouble knowing the depth (Thornton, 1987). The classic case of a mountain can be presented to clarify this idea because it is easy to see the height of the mountain and know how wide it is by sight alone but to realize that the mountain also has a certain depth and also extends deep into the ground has to come from the inferences made by the mind.

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When we dream the world we enter is one that has laws and rules (though sometimes different than the real world), and yet we can tell the difference. But what is reality was being hidden from us. The Matrix suggests that there is a sub-world, something else beneath the actual world we live in.

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