Let A 5 k 0 5 Then A is diagonalizable exactly for the foll

Let A = [5 k 0 5] Then A is diagonalizable exactly for the following values of k select one of the options, fill in the corresponding answer blanks, if any, and leave the remaining answer blanks empty? all k all k except k = 0 only for k = no values of k ii) Let B = [5 k 0 1] Then B is diagonalizable exactly for the following values of k select one of options, fill in the corresponding answer blanks, if any, and leave the remaining answer blanks empty. all k all k except k = only for k = no value of k =

Solution

1.

for a matrix to be diagonalizable determinant of matrix should not be zero.

det A = 5*5 - 0*k

det A = 25 - 0 = 25

det A will never be zero since it doesn\'t depend on the value of k.

it will be diagonalizable for all values of k.

2.

for a matrix to be diagonalizable determinant of matrix should not be zero.

det B = 5*1 - 0*k

det B = 5 - 0 = 5

det B will never be zero since it doesn\'t depend on the value of k.

it will be diagonalizable for all values of k.