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Let 
, where 
, and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP - I3)2 is αω2 , then the value of α is equal to _________.
, where , and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP - I3)2 is αω2 , then the value of α is equal to _________.Correct answer is '36'. Can you explain this answer?
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Most Upvoted Answer
Let,where,and I3 be the identity matrix of order 3. If the determinant...
Let M = (P-1AP - I)2
= (P-1AP)2 - 2P-1AP + I
= P-1A2P - 2P-1AP + I
PM = A2P - 2AP + P
= (A2 - 2A.I + I2)P
Det(PM) = Det((A - I)2 × P)
DetP.DetM = Det(A - I)2 × Det(P)
DetM = (Det(A - I))2
Now
Det(A - I) = (w2 + w + w) + 7(-w) + w3 = -6w
Det((A - I))2 = 36w2
α = 36
= (P-1AP)2 - 2P-1AP + I
= P-1A2P - 2P-1AP + I
PM = A2P - 2AP + P
= (A2 - 2A.I + I2)P
⇒
⇒
⇒
Now
Det(A - I) = (w2 + w + w) + 7(-w) + w3 = -6w
Det((A - I))2 = 36w2
⇒
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Let,where,and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP - I3)2 isαω2 , then the value of αis equal to _________.Correct answer is '36'. Can you explain this answer?
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Let,where,and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP - I3)2 isαω2 , then the value of αis equal to _________.Correct answer is '36'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let,where,and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP - I3)2 isαω2 , then the value of αis equal to _________.Correct answer is '36'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let,where,and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP - I3)2 isαω2 , then the value of αis equal to _________.Correct answer is '36'. Can you explain this answer?.
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