Let A be a matrix 2 0 0 0 0 0 0 0 2 I got the problem wrong

Let A be a matrix = 2 0 0

0 0 0

0 0 2

I got the problem wrong so please look at my answers.

thank you

Solution

a) For finding the transformation from R^3 ------> R^3

Multiplying the matrix with x,y,z we get the vector as (2x,0,2z), which means that the y coordinate will always be equal to zero

Hence the transformation will be from (x,y,z) to (x,0,z) it will lie on the xz plane where the value of y will be equal to zero

c) The basis of RSA is equal to [1,0,0] and [0,0,1]

d) Eigen vectors of TA will be [1,0,0] and [0,0,1]

e) Eigen values of TA

Determinant of A = (2-x)[x(x-2)]

=> (2-x)(x)(x-2)

The value of x = 0 is the first eigen value and x=2 is the second eigen value, hence there are only two possible eigen values for this matrix

But x=0 is considered as null eigen value