Homework SourseFind an invertible matrix P and a matrix C of the form a b b
Find an invertible matrix P and a matrix C of the form [a b -b a] such that A = [0.6 2 -0.4 -0.2] has the form A = PCP^-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrices P and C are. (Use a comma to separate answers as needed.) B. There is no matrix C of the form [a b -b a] and no invertible matrix P such that A = PCP^-1.![Find an invertible matrix P and a matrix C of the form [a b -b a] such that A = [0.6 2 -0.4 -0.2] has the form A = PCP^-1 Select the correct choice below and,](/WebImages/39/find-an-invertible-matrix-p-and-a-matrix-c-of-the-form-a-b-b-1118966-1761595006-0.webp "Find an invertible matrix P and a matrix C of the form [a b -b a] such that A = [0.6 2 -0.4 -0.2] has the form A = PCP^-1 Select the correct choice below and,")
Solution
the matrix A = 1/10 [ 6 -4
20 -2]
C is the diagonal matrix whose entries a re the real eigen values of the matrix A
| A -kI| =0 where k is the eigen value
| 6-k -4
20 -2-k| =0
=> (6-k) ( -2-k) +80=0
=> k2-4k+80 =0 the roots are imaginary , no real roots hence matrix C doesnt exist
