Linear Transformations

Forums Leaving Cert Maths Linear Transformations

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    • #1671

      i dont understand honours maths linear transformations at all….. nobody can explain them. if any1 knws a simple method or even another website dat cn help. my teacher cnt explain dem or my grinds teacher :? :O
      thanx :)

    • #17315

      are you referring to the line transformation of points or the triangle which contains of lines right. and each of there points contain coordinates..??/ if so message me and i got pretty idea how to do it….

    • #17316

      its the line transformations of points….. if u cud help i wud b sooooooooooo happy. thanx!!!! :D

    • #17317

      Hang in there. I had a full suggestion for approaching linear transfns typed in when the page expired. You will have an explanation by about 10am, Thurday morning

    • #17318

      The secret of linear tranfns. is not revealed in text-books nor usually, alas, in class. It is this:
      There are two planes, one is the ordinary x-y plane (that’s a dash between x and y, not a minus sign), the other plane is an exact copy but is called the x’-y’ plane. To understand linear transfns you MUST do this: draw two perp. axes on the left side of your page. Label them x and y. This is the usual x-y plane
      To the right of this write the letter f and underneath it an arrow –> pointing right. To the right of the arrow draw two perp. axes. Label them x’ and y’. This will be the x’-y’ plane. You’re ready.
      f is a magic wand that changes pretty shapes (like circles) in the x-y plane into ugly shapes in the x’-y’ plane. The arrow shows you in which direction this ‘magic’ flows. However because f is a LINEar transfn. it has mercy on lines (they’re kin after all) and only kicks them around a bit but doesn’t change their shape.
      For example, a certain f that will be revealed later takes the line 4x – y + 5 =0 which slopes upwards in the x-y plane and changes it to a line 2x’ + y’ + 6 = 0 that slopes downwards in the x’-y’ plane!
      To check this claim, draw the line 4x – y + 5= 0 in the x-y plane. It slopes upwards, right? Now draw 2x’ + y’ + 6=0 in the x’-y’ plane. It slopes downwards, right? (If you don’t know how to draw a line from its equation, ask, but the easiest way is to let x =0 first and find y, then let y = 0 and find x).
      I know which f works this wicked wonder because I made up the question. Here it is : x’ = 2x and y’ = -y – 1. There’s a reason why f is written this way but that’s for another time.
      The Leaving Cert concentrates on getting you to find the equation of the x’-y’ line in the x’-y’ plane, given the x-y line and the magic f. The method is in all the books but if I can help with it I will
      Meanwhile, if you don’t do as I advise and draw those two planes with f and the –> between them you’re just not going to get this stuff.

      If you want more, ask a specific question if possible. Otherwise, beir bua.

    • #17319

      sorry… i knw its been 15 weeks but i havent been on this in a while. it wudnt let me go onto it on my computer! thanx sooooooooooooooooooooooo much. it was really helpful! :)

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