Please help ASAP. C is written as the 4 by 4 matrix, as: 1 -1 0 0 0 1 -1 0 0 0 1

Question

Please help ASAP. C is written as the 4 by 4 matrix, as: 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 1 If J is the Jordan canonical form of C, find P or its inverse(whichever is more convienent) satisfying as CP-1 (P ^ -1) = P-1J(P^-1) * J So, what I have so far is: - Characteristic polynomial = (x-1) ^ 4 - Minimal polynomial = (x-1) ^ 4 - Jordan block = (1,1,0,0; 0, 1, 1, 0; 0, 0, 1, 1; 0,0,0,1] How do you find P based on this??? HELP! Please help ASAP. C is written as the 4 by 4 matrix, as: 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 1 If J is the Jordan canonical form of C, find P or its inverse(whichever is more convienent) satisfying as CP-1 (P ^ -1) = P-1J(P^-1) * J So, what I have so far is: - Characteristic polynomial = (x-1) ^ 4 - Minimal polynomial = (x-1) ^ 4 - Jordan block = (1,1,0,0; 0, 1, 1, 0; 0, 0, 1, 1; 0,0,0,1] How do you find P based on this??? HELP!

Explanation / Answer

The inverse is easier to find. Place the matrix next to the identity matrix then performing thesame operations on both until you get the identity matrix in theplace of the original. The operations are: R4+R3->R3'+R2->R2'+R1 = 1 1 1 1 0 1 1 1 0 0 11 0 0 01

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