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Transforming vectors using matrices

Sal transforms a 2-dimensional vector using a 2x2 matrix, and draws the original vector and its image on the plane. Created by Sal Khan.

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• What's the meaning of a transformation matrix? What does it represent?
• At what did Sal mean by saying 'P Prime'?
I'm a bit confused at that part, could someone please explain it to me?
Thanks!
• P is the original vector.
P' is the transformed vector.
He could have called the transformed version of vector P P1 or Pt, just as to differentiate it from the original vector. Often the ' symbol is used to denote a transformation of a variable by some process.
Very soon you will learn a very different meaning for the symbol ' within the context of differential calculus.
(1 vote)
• Can there be variables in matrices?
And if so, Can there be matrix equations?
Ex:
`[ 3 5 ] [ 3 5 ] [ 4 x ] = [ 9 -5 ] [ 3 3 ] [ 1/2 5 ]`

Note: The separate square brackets are actually for 3 X 3 matrices.
• What do the values in the transformation matrix mean? i.e in case of the vector's column matrix, 2 is the x component whereas 1 is the y component, so in a similar fashion what do the values in transformation matrix signify? How do they tell that x-component should translate to 5 and y component to 0?
• How can we actually determine the Transformation matrix?
• We get to pick whatever transformation matrix we want depending on our particular goal. See the remaining videos of this section.
• In the P column matrix of order 2 cross 1, in the above video, how do we figure out which number is x and which one is y?
• it is conventional that first is X and next one is Y. Thus P_{1,1 } is X and P_{2,1} is Y