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If a square matrix M has a stable distribution, then it must be regular

If a square matrix M has a stable distribution, then it must be regular

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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please send solution for Q10 only handwritten solution accepted
For each question: - Clearly state: True or False - If True, provide a concise explanation - If False, provide an explicit counterexample 1. Let A = b be a consistent, inhomogeneous system of linear equations. A solution to the system is given by i = A- 2. Let S, T C R" with S being a proper subset of T. If span(S) = span(T), then T is linearly dependent. 3. Let S C P(R) be the set of all even degree polynomials. Then S forms a subspace of P(R). 4. Consider two maps S, T : R" R". The composition SoT is a linear map if and only if both S and T are linear maps 5. Any invertible 3 x 3 real matrix M is a matrix of change of basis [C]g for some bases B and C. 6. Let W be a finite dimensional subspace of an inner product space V. For each w e W, there exists a unique v EV such that w is an orthogonal projection of v on W. 7. Let A be a 4 x 4 matrix such that the homogeneous equation Af = õ has general solution i = Xữ for some non-zero vector TER. Then, rank(A) = 3. %3D 8. Let V be a inner product space and let a e V be a non-zero vector. The subset U defined by U = {ie V(F, ā) = 0} is a subspace of V 9. If A ER is a common eigenvalue of two n x n matrices A and B, then A is also an eigenvalue of A+ B. 10. If a square matrix M has a stable distribution, then it must be regular
Transcribed Image Text:For each question: - Clearly state: True or False - If True, provide a concise explanation - If False, provide an explicit counterexample 1. Let A = b be a consistent, inhomogeneous system of linear equations. A solution to the system is given by i = A- 2. Let S, T C R" with S being a proper subset of T. If span(S) = span(T), then T is linearly dependent. 3. Let S C P(R) be the set of all even degree polynomials. Then S forms a subspace of P(R). 4. Consider two maps S, T : R" R". The composition SoT is a linear map if and only if both S and T are linear maps 5. Any invertible 3 x 3 real matrix M is a matrix of change of basis [C]g for some bases B and C. 6. Let W be a finite dimensional subspace of an inner product space V. For each w e W, there exists a unique v EV such that w is an orthogonal projection of v on W. 7. Let A be a 4 x 4 matrix such that the homogeneous equation Af = õ has general solution i = Xữ for some non-zero vector TER. Then, rank(A) = 3. %3D 8. Let V be a inner product space and let a e V be a non-zero vector. The subset U defined by U = {ie V(F, ā) = 0} is a subspace of V 9. If A ER is a common eigenvalue of two n x n matrices A and B, then A is also an eigenvalue of A+ B. 10. If a square matrix M has a stable distribution, then it must be regular
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