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be a matrix with real entries. If the sum and the product of all the eigenvalues of A are 10 and 30, respectively, then a2 + b2 equals ____
be a matrix with real entries. If the sum and the product of all the eigenvalues of A are 10 and 30, respectively, then a2 + b2 equals ____Correct answer is '29'. Can you explain this answer?
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Verified Answer
Letbe a matrix with real entries. If the sum and the product ofall the...
Characteristic polynomial of A = t2 - tr(A) + |A| = t2 - ( a + b + 3)t + 3ab
Sum of eigen values = 10
and product of eigenvalues = 30
Then, t2 - ( a + b + 3) t + 3ab = t2 - 10t + 30
⇒ a+b + 3 = 10
a + b = 7 and
3ab = 30 ⇒ ab = 10
a2 + b2 = ( a + b)2 - 2ab
= ( 7)2- 2 x 10 = 49 - 20 = 29
Sum of eigen values = 10
and product of eigenvalues = 30
Then, t2 - ( a + b + 3) t + 3ab = t2 - 10t + 30
⇒ a+b + 3 = 10
a + b = 7 and
3ab = 30 ⇒ ab = 10
a2 + b2 = ( a + b)2 - 2ab
= ( 7)2- 2 x 10 = 49 - 20 = 29
Most Upvoted Answer
Letbe a matrix with real entries. If the sum and the product ofall the...
Characteristic polynomial of A = t2 - tr(A) + |A| = t2 - ( a + b + 3)t + 3ab
Sum of eigen values = 10
and product of eigenvalues = 30
Then, t2 - ( a + b + 3) t + 3ab = t2 - 10t + 30
⇒ a+b + 3 = 10
a + b = 7 and
3ab = 30 ⇒ ab = 10
a2 + b2 = ( a + b)2 - 2ab
= ( 7)2- 2 x 10 = 49 - 20 = 29
Sum of eigen values = 10
and product of eigenvalues = 30
Then, t2 - ( a + b + 3) t + 3ab = t2 - 10t + 30
⇒ a+b + 3 = 10
a + b = 7 and
3ab = 30 ⇒ ab = 10
a2 + b2 = ( a + b)2 - 2ab
= ( 7)2- 2 x 10 = 49 - 20 = 29
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Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer?
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Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer?.
Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Letbe a matrix with real entries. If the sum and the product ofall the eigenvalues of A are 10 and 30, respectively, then a2 + b2equals ____Correct answer is '29'. Can you explain this answer?.
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