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Linear Algebra: Should I multiply these two translation matrices together?

If I have 2 translation matrices.

Matrix A: Translates 2 units up the Y axis.

Matrix B: Translates 3 units up the Y axis, and 2 units up the X axis.

If I multiple these two matrices together, will the resulting matrix translate 5 units up the Y axis, and 2 units up the X axis?

That is my goal, and apparently I'm just enough years beyond Linear algebra to remember.

Thanks!
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oxygen_728
Asked:
oxygen_728
2 Solutions
 
ozoCommented:
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Ehsan_NoureddinCommented:
Yes , Exactly ..
if you have a 3D vector for translating and rotating you must add one row to your matrix i will show you :


      | X |
V = | Y |
      | Z |
      | 1 |

Translatin Matrix for translating a,b,c is :

Trans = | 1 0 0 a |
            | 0 1 0 b |
            | 0 0 1 c |
            | 0 0 0 1 |

now if you Multiple your Vector to Trans Matrix the Result Matrix is  :

New V = | X+a  |
             | Y+b  |
             | Z+c  |
             | 1      |

Now you Can Remove the added Row ..
is it you answer ?


and for Trans 2 o 3 o more time you just need to translate the result again and again ..
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oxygen_728Author Commented:
Thanks for the tips!
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