tag:blogger.com,1999:blog-49922555515790053272016-09-07T21:34:02.808-07:00Math and NLPMariana Sofferhttp://www.blogger.com/profile/13351209522681966230noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-4992255551579005327.post-22619451751633466472009-03-10T17:47:00.000-07:002009-03-10T17:48:58.998-07:00Inverse Matrix<h3 class="post-title entry-title"> <a href="http://mathsisinteresting.blogspot.com/2008/08/inverse-matrix-what-is-it-used-for.html">What is it used for?</a> </h3> <div class="post-body entry-content"> One of the applications of inverse matrix is in solving simultaneous equations.<br /><br />If you are good with algebra, you will discover that this inverse matrix way of handling the solution of simultaneous equations is similar, except that they are done as a group, collectively.<br />The answers to the unknown variables are obtained at one go with this Inverse matrix method.<br /><br />However, what do you need to know in order to use this Inverse matrix solving?<br /><br />You have to understand:<br />1) Convertion of simultaneous equations into a <strong>set of matrices</strong><br />2) <strong>Determinant</strong> and technique to get its numerical value<br />3) <strong>Minor</strong> of the individual elements within the matrix<br />4) <strong>Co-factor</strong> of this determinant formed with this set of matrices<br />5) <strong>Transpose</strong> of matrix<br />6) <strong>Adjoint matrix</strong> obtained with the co-factors and transposed matrix<br />7) Formula to relate determinant with the adjoint matrix ==> <strong>Inverse matrix</strong><br />8) Matrices <strong>multiplication</strong><br /><br />The list looks amazingly long for matrix novice, but, DO NOT FEAR!<br /><br />Why?<br />Matrices consist of numbers only, and simple mathematical operations, nothing abstract.<br />(The details are not presented here for fear that you will leave this site.)<br /><br />Slowly research into the above terms and see for yourself that they are "friends" and not "foes".<br /><br />Happy start to matrices and its application.<br /></div> <!-- spacer for skins that want sidebar and main to be the same height-->Mariana Sofferhttp://www.blogger.com/profile/13351209522681966230noreply@blogger.com9tag:blogger.com,1999:blog-4992255551579005327.post-35586397980962555912009-03-10T17:08:00.000-07:002009-03-10T17:10:07.170-07:00Basic Trigonometric<h3 class="post-title entry-title"> <a href="http://sk19math.blogspot.com/2007/06/trigonometric-identities.html">Trigonometric Identities - Basic Identities</a> </h3> Trigonometric identities are specific equalities that express one trig function in terms of other trig functions. They are fairly straightforward, but they take some work to derive them. If you are comfortable with simple derivations, you shouldn't have any problems though. Personally, I find it easier to remember the basic set of identities, and derive the more complex ones from those, rather than trying to memorize all of them... although some people are more comfortable just to memorize them.<br /><br />The basic identities are traditionally visualized with a triangle formed by a radius r, length x, and height y:<br />The basic trig definitions can easily be seen:<br /><div style="text-align: left;">Sin(theta) = y/r..... opposite/hypotenuse<br />Cos(theta) = x/r..... adjacent/hypotenuse<br />Tan(theta) = y/x..... opposite/adjacent<br /></div><br /><div style="text-align: left;">If we now apply the Theorem of Pythagoras, we can see:<br /></div><div style="text-align: center;">r^2 = x^2 + y^2<br /></div><div style="text-align: left;">Dividing everything by r^2 gives:<br /></div><div style="text-align: center;">1 = (x^2)/(r^2) + (y^2)/(r^2)<br />1 = (x/r)^2 + (y/r)^2<br /><div style="text-align: left;">And then, subbing in the basic definitions, we get:<br /><div style="text-align: center;">1 = [Cos(theta)]^2 + [Sin(theta)]^2<br /><div style="text-align: left;"><br />And that is the first basic identity. Nothing to it. It's proper name is the Pythagorean Trigonometric Identity. I'll rewrite it in proper notation to clean it up a bit... (Blogger is a pain with superscripts and fonts)<br /><div style="text-align: center;"><br /></div></div></div></div></div>Another basic relationship starts with:<br />Tan(theta) = y/x<br />But, then sub in the Sine and Cosine definitions (isolated for x and y, respectively) to give<br />Tan(theta) = (r*Sin(theta)) / (r*Cos(theta))<br />Tan(theta) = Sin(theta) / Cos(theta)<br /><br />And that's it again. This is called the Ratio Identity:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_ufoH7a6Pb_E/RuoF8GFqZKI/AAAAAAAAAFY/7CmXMRfktU4/s1600-h/untitled.JPG"><img style="cursor: pointer;" src="http://3.bp.blogspot.com/_ufoH7a6Pb_E/RuoF8GFqZKI/AAAAAAAAAFY/7CmXMRfktU4/s320/untitled.JPG" alt="" id="BLOGGER_PHOTO_ID_5109903257189901474" border="0" /></a><br />Those are now two of the simplest trig identities from which most of the others can be derived.Mariana Sofferhttp://www.blogger.com/profile/13351209522681966230noreply@blogger.com3