Writing Equations Using Number Manipulations

The word and is equivalent to addition difference refers to subtraction. It s the variations on and the subtle use of these words that affect how the mathematical expression is written. Look at the following interpretations. 

The subtleties in the wording are important in the interpretation. The implied grouping symbols need to be written when translated into mathematics. The English language can be misinterpreted (in world relations, too, of course), so it s usually a good idea to use as many descriptive words as necessary to be sure that your mathematical meaning is understood. 

Many algebra word problems involve a single number and some operations performed on it. The problems of this sort are good for practice in writing algebraic equations, because you only need to worry about one unknown, or variable. For simplicity, I ll use x for the unknown. 

The translations from word problems to algebraic problems have two standard rules  

Let the number be represented by x. The word sum implies addition, so add the x and 12. Put an equal sign after the sum and before the 18. The equation you want reads x + 12 = 18. Solving this linear equation, you subtract 12 from each side to get x = 6. Now, check your answer. Replace a number in the problem with 6, and it now reads The sum of 6 and 12 is 18. You got it  

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In Section 4.1 the matrix notation was first introduced for writing a set of linear equations. However, the discussion there rapidly moved to a discussion of linear equations and the solution techniques developed were based upon Gauss elimination teehniques and did not direetly use matrix manipulation techniques. For a number of engineering problems the manipulation of matrix equations is the most eonvenient approaeh so this seetion will discuss and develop some numerical techniques for direct matrix manipulation. Going back to the matrix formulation of a set of linear equations (as Eq. (4.5)) one has ... 

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