In a sentence give a geometric interpretation of the followi

In a sentence, give a geometric interpretation of the following transformation: T([x y]) = [r 0 0 r] [x y], where r > 1 Using the definition of an eigenvalue, determine whether or not A -eigenvalue of the following matrix: [2 0 9 -2 5 8 -8 -7 0 0 70 6 0 7 9]

Solution

Mutiplying a column matrix (x y)^T a square matrix that is r times Identity matrix means that we are obtaining a column matrix who elements have been multiplied by a constant term \'r\'; This is similar to writing a matrix A as rA; Its location has been extended by \'r\' times from the origin, in the same direction;