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Problem 6. Decide whether the following statements are True or False. each correct explanation a) If A, B are two n x n matrices, then nullity of A is less or equal to the nullity of AB. b) If A is a symmetric 4 x 4 matrix with characteristic polynomial fA(^) = X²(A – 1)(A – 2), then the kernel A is 2-dimensional. c) T(7) = A is a linear transformation of R³ to itself with det(A) = 3. Let S be the unit square generated by ej : , e2 Then the area of T(S) is 3. -5] The zero state is an asymptotically stable equilibrium solution of -3 d) A = -4 180 the system Az. dt e) The curve defined by x + 6xy +7y² = 2015 is an ellipse in R?.

Problem 6. Decide whether the following statements are True or False. each correct explanation a) If A, B are two n x n matrices, then nullity of A is less or equal to the nullity of AB. b) If A is a symmetric 4 x 4 matrix with characteristic polynomial fA(^) = X²(A – 1)(A – 2), then the kernel A is 2-dimensional. c) T(7) = A is a linear transformation of R³ to itself with det(A) = 3. Let S be the unit square generated by ej : , e2 Then the area of T(S) is 3. -5] The zero state is an asymptotically stable equilibrium solution of -3 d) A = -4 180 the system Az. dt e) The curve defined by x + 6xy +7y² = 2015 is an ellipse in R?.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 6. Decide whether the following statements are True or False. each correct explanation a) If A, B are two n x n matrices, then nullity of A is less or equal to the nullity of AB. b) If A is a symmetric 4 x 4 matrix with characteristic polynomial fa(^) = X²(A– 1)(A – 2), then the kernel A is 2-dimensional. c) T(7) = AF is a linear transformation of R³ to itself with det(A) 3. Let S be the unit square generated by ei Then the area of T(S) is 3. -3 d) A The zero state is an asymptotically stable equilibrium solution of 4 180 the system = A7. dt e) The curve defined by x? + 6xy + 7y² = 2015 is an ellipse in R².
Transcribed Image Text:Problem 6. Decide whether the following statements are True or False. each correct explanation a) If A, B are two n x n matrices, then nullity of A is less or equal to the nullity of AB. b) If A is a symmetric 4 x 4 matrix with characteristic polynomial fa(^) = X²(A– 1)(A – 2), then the kernel A is 2-dimensional. c) T(7) = AF is a linear transformation of R³ to itself with det(A) 3. Let S be the unit square generated by ei Then the area of T(S) is 3. -3 d) A The zero state is an asymptotically stable equilibrium solution of 4 180 the system = A7. dt e) The curve defined by x? + 6xy + 7y² = 2015 is an ellipse in R².
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