Question

Find an invertible matrix P and a matrix C of the form a -b 1.4 -0.8 such that A= has the form A =PCP-1 b a 4 - 1.8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrices P and Care (Use a comma to separate answers as needed.) ов. a -b There is no matrix C of the form and no invertible matrix P such that A = Pcp-1 b a

Answer 1

Using matrix multiplication rule we solve the given problem.
Here 1.4 -0.8 4 -1.8 Let, pa b, al bi a, Ca az -6,7 ь, а, A = Pcp' multiplying Since both side by P > (A Jp = pc o'p → AP= PCC plo) ЗАр = pc -a-bi را - ره- ba az [ 11:9][3) [ 11 [li 1.4a-08b, -1.46,-0.8a, 49,-1e8b, - 4b,-1.89, -ala-b, bz - bza, - a₂ by az bi tayb2 - b, b, tay 92 1.40 -0.8 b = 2/92 - bb2 491-118 by a a2 bit ab. -1461 -0.8a - b₂a-b, az (3 -461 - 1.89 = -bib, tapa2 Adding B and 6 1.40 - 0.8 bi y bar 180 = 4 aa-b, bab, bata,a2 Ź.401 – 418 61 = 0 -41 +418b, > a = 4.8 y = -12 bi +6

Adding ① and ② ya - 1.8 b, - 1.4b, orgaz az bi tay b2 - bgay-b, a 3.294-3.2b, = 0 → 3.204 = 3.2b by from 6 and 6 it shows that no invertible matrix p exist. also Thore is no matrix e of the form [ab] invertible and No . There is no matrix e of the form [a b] matrixp such that A-PCP option ® is correct.