Find the smallest integer value for k such that the linear operator T:R 3 ⟶R 3 given by T(x,y,z)=(x+y+kz, x+y−z, x+y+z) is dagonalizable . Then for the value of k found, determine a diagonal matrix...

Find the smallest integer value for k such that the linear operator T:R₃⟶R₃
given by T(x,y,z)=(x+y+kz, x+y−z, x+y+z) is dagonalizable . Then for the value of k found, determine a diagonal matrix similar to the matrix of the operator T in the canonical basis of R3.