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Consider a matrix 
The matrix A satisfies the equation 6A-1 = A2 + cA + dI, where c and d are scalars and I is the identity matrix. Then (c + d) is equal to
The matrix A satisfies the equation 6A-1 = A2 + cA + dI, where c and d are scalars and I is the identity matrix. Then (c + d) is equal to
- a)5
- b)17
- c)-6
- d)11
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI...
Concept:
for the given square matrix, the characteristic equation will be
|B - AI| = 0
B = Given matrix
I = Unit matrix
A = Characteristic roots
Calculation:
|B - AI| = 0
Take the determinant of matrix, then
(1 - A) [(4 - A) (1 - A) + 2] = 0
(1 - A) [4 - 4A - A + A2 + 2] = 0
(1 - A) [4 - 5A + A2 + 2] = 0
(1 - A) [A2 - 5A + 6] = 0
A2 - 5A + 6 - A3 + 5A2 - 6A = 0
-A3 + 6A2 - 11A + 6 = 0
A3 - 6A2 + 11A = 6
A2 - 6A + 11 = 6A-1 ........(1)
Given 6A-1 = A2 + cA + dI .........(2)
Compare 1 and 2
c = -6, d = +11
c + d = +5
Most Upvoted Answer
Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI...
Concept:
for the given square matrix, the characteristic equation will be
|B - AI| = 0
B = Given matrix
I = Unit matrix
A = Characteristic roots
Calculation:
|B - AI| = 0
Take the determinant of matrix, then
(1 - A) [(4 - A) (1 - A) + 2] = 0
(1 - A) [4 - 4A - A + A2 + 2] = 0
(1 - A) [4 - 5A + A2 + 2] = 0
(1 - A) [A2 - 5A + 6] = 0
A2 - 5A + 6 - A3 + 5A2 - 6A = 0
-A3 + 6A2 - 11A + 6 = 0
A3 - 6A2 + 11A = 6
A2 - 6A + 11 = 6A-1 ........(1)
Given 6A-1 = A2 + cA + dI .........(2)
Compare 1 and 2
c = -6, d = +11
c + d = +5
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Community Answer
Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI...
Concept:
for the given square matrix, the characteristic equation will be
|B - AI| = 0
B = Given matrix
I = Unit matrix
A = Characteristic roots
Calculation:
|B - AI| = 0
Take the determinant of matrix, then
(1 - A) [(4 - A) (1 - A) + 2] = 0
(1 - A) [4 - 4A - A + A2 + 2] = 0
(1 - A) [4 - 5A + A2 + 2] = 0
(1 - A) [A2 - 5A + 6] = 0
A2 - 5A + 6 - A3 + 5A2 - 6A = 0
-A3 + 6A2 - 11A + 6 = 0
A3 - 6A2 + 11A = 6
A2 - 6A + 11 = 6A-1 ........(1)
Given 6A-1 = A2 + cA + dI .........(2)
Compare 1 and 2
c = -6, d = +11
c + d = +5
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Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer?
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Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer?.
Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a matrixThe matrix A satisfies the equation 6A-1= A2+ cA + dI, where cand dare scalars and Iis the identity matrix. Then (c+ d) is equal toa)5b)17c)-6d)11Correct answer is option 'A'. Can you explain this answer?.
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