please solve Q4 step step only handwritten solution accepted For each question:- Clearly state: True or False- If True, provide a concise explanation- If False, provide an explicit counterexample1. Let A = b be a consistent, inhomogeneous system of linear equations. A solution to the systemis 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 linearlydependent.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 bothS and T are linear maps5. 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, thereexists 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 solutioni = Xữ for some non-zero vector TER. Then, rank(A) = 3.%3D8. Let V be a inner product space and let a e V be a non-zero vector. The subset U defined byU = {ie V(F, ā) = 0}is a subspace of V9. If A ER is a common eigenvalue of two n x n matrices A and B, then A is also an eigenvalueof A+ B.10. If a square matrix M has a stable distribution, then it must be regular

4. Consider two maps S,T:IRn→IRnThe composition SoT is a linear map ifboth S and T are linear maps

Answered: 4. Consider two maps S,T: R" R". The…

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4. Consider two maps S,T: R" R". The composition So T is a linear map if and only if both S and T are linear maps

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 2BEXP

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