Movement of a vector when multiplied by a matrix

[Ali Asadullah]

What is the effect on a vector when it is multiplied by a matrix?
Let any matrix
2 3
3 5
What will be the effect on vectors when they are multiplied with this matrix?
In which direction will they move?
What will be the effect of multiplying vectors with any matrix of order n by n?

 

[Mark44]

Different vectors are affected differently when multiplied by a given matrix. If the vector being multiplied by the matrix happens to be an eigenvector, the result vector is a vector in the same (or opposite) direction, scaled by the value of the eigenvalue associated with this eigenvector.

 

[Ali Asadullah]

Let a matrix
1 1
1 1
If we multiply all the points/vectors in a plane with this matrix, what will be the resultant?

 

[berkeman]

Let a matrix
1 1
1 1
If we multiply all the points/vectors in a plane with this matrix, what will be the resultant?

What happens if you try some examples? Can you show us a few examples that you have worked out?