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.

Re: Simple Linear Algebra Question

Quote:

Originally Posted by

**allyourbass2212** 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:

$\displaystyle \frac54\div3 = \frac54\div\frac31 = \frac54\cdot\frac13.$

Re: Simple Linear Algebra Question

Quote:

Originally Posted by

**Reckoner** 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 $

Re: Simple Linear Algebra Question

Quote:

Originally Posted by

**allyourbass2212** 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.

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

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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