The matrix A in the linear transformation y = Ax and the eigen vector and eigen values with the explanation of their geometric meaning if R 3 is projected orthogonally onto the plane x 2 = x 1 . The matrix A in the linear transformation y = Ax is [ 1 2 1 2 0 1 2 1 2 0 0 0 1 ] _ . The eigen values are 0 and 1 _ . The eigen vectors are [ 1 − 1 0 ] T _ , [ 0 0 1 ] and [ 1 1 0 ] _ . It is given that x = [ x 1 x 2 ] T ( x = [ x 1 x 2 x 3 ] T ) are cartesian coordinates. The matrix obtained when R 3 is projected orthogonally onto the plane x 2 = x 1 is obtained as shown below: [ 1 2 1 2 0 1 2 1 2 0 0 0 1 ] From the above matrix, the eigen values is 1 _ with the eigen vectors [ 0 0 1 ] and [ 1 1 0 ] _ From the eigen vectors, it is obtained that every point in the plane y = x is mapped onto itself. Also, the othe eigen value is 0 _ with the eigen vector [ 1 − 1 0 ] T _ . Hence, any point on the line y = − x , z = 0 is mapped on to the origin.

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