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Thread: Simple Linear Algebra Question

  1. #1
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    Simple Linear Algebra Question

    Equation: $\displaystyle 3t= \frac{5}{4}$

    Step 1: $\displaystyle t=\frac{1}{3}*\frac{5}{4}$

    My question concerns this step. To isolate the variable "t" you divide by 3. It seems that should read $\displaystyle t=\frac{5}{4} \div \frac{1}{3}$ however that leads to an incorrect answer. The correct way to do this apparently is $\displaystyle t=\frac{1}{3}*\frac{5}{4}$. Why do you multiply by 1/3? When you isolate "t" you divide by 3.


    Thanks for the clarification.
    Last edited by allyourbass2212; Jul 12th 2012 at 07:54 AM.
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    Re: Simple Linear Algebra Question

    Quote Originally Posted by allyourbass2212 View Post
    My question concerns this step. To isolate the variable "t" you divide by 3. It seems that should read $\displaystyle t=\frac{5}{4} \div \frac{1}{3}$
    No, here you are trying to divide by $\displaystyle \textstyle\frac13,$ not 3. Dividing by three is the same as multiplying by one-third:

    $\displaystyle \frac54\div3 = \frac54\div\frac31 = \frac54\cdot\frac13.$
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    Re: Simple Linear Algebra Question

    Quote Originally Posted by Reckoner View Post
    No, here you are trying to divide by $\displaystyle \textstyle\frac13,$ not 3. Dividing by three is the same as multiplying by one-third:

    $\displaystyle \frac54\div3 = \frac54\div\frac31 = \frac54\cdot\frac13.$
    Thanks, to be clear then this is for all linear algebra for instance

    Equation:$\displaystyle 2x = 6$
    Step 1: $\displaystyle x= \frac{6}{1} \cdot \frac{1}{2}$
    $\displaystyle x= 3 $
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    Re: Simple Linear Algebra Question

    Quote Originally Posted by allyourbass2212 View Post
    Equation:$\displaystyle 2x = 6$
    Step 1: $\displaystyle x= \frac{6}{1} \cdot \frac{1}{2}$
    $\displaystyle x= 3 $
    Correct. You could work this either way, by dividing both sides by 2 or by multiplying both sides by the reciprocal $\displaystyle \textstyle\frac12.$ You get the same result regardless.
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    Re: Simple Linear Algebra Question

    attraction signs





    tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspxHere are my online notes for my Linear Algebra course that I teach here at ... Sometimes a very good question gets asked in class
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    Re: Simple Linear Algebra Question

    Simple linear algebra is a integrated part of mathematics. sometimes students ask a difficult and logical questions in the class.

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