Check the true statements below: OA. det AT = (-1)detA. OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, a3. OC. If one multiple of one row of A is added to another row, the eigenvalues do not change. D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k. %3D
Check the true statements below: OA. det AT = (-1)detA. OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, a3. OC. If one multiple of one row of A is added to another row, the eigenvalues do not change. D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k. %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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Question
A and B are n x n matrices
![Check the true statements below:
OA. det A™
OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, az.
C. If one multiple of one row of A is added to another row, the eigenvalues do not change.
D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k.
(-1)det A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe1ce3ee-9943-4672-ac98-a0fbedd4e0d2%2F3a2a56cc-b5f5-4d67-82ad-ce78f27515cc%2Fq7ex4cf_processed.png&w=3840&q=75)
Transcribed Image Text:Check the true statements below:
OA. det A™
OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, az.
C. If one multiple of one row of A is added to another row, the eigenvalues do not change.
D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k.
(-1)det A.
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