I was reading Linear Algebra by Hoffman and Kunze and I encountered some concepts which were arguabl

Aman Wyatt 2022-02-23 Answered
I was reading Linear Algebra by Hoffman and Kunze and I encountered some concepts which were arguably not explained or expounded upon thoroughly. I will present my questions below, and I am looking for answers that do not invoke concepts like determinant, vector spaces etc. Note that this is an introductory chapter that assumes no knowledge of the above concepts.
Question 1: Consider a linear system A with k equations. If we form a new equation by taking a linear combination of these k equations, then any solution of A is also a solution of this new equation. Why is this so?
Question 2a: Consider two linear systems A and B. If each equation of A is a linear combination of the equations of B, then any solution of B is also a solution of A. Why is this so?
Question 2b: If each equation of A is a linear combination of the equations of B, then it is not necessary that any solution of A is also a solution of B. Why is this so?
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Elsie Tillman
Answered 2022-02-24 Author has 5 answers
1) If a=b and c=d, then sa+tc=sb+td.
2a) Apply 1) to each equation of A.
2b) For example, 0=0 is a linear combination of a=b and a=b.
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ozebnikvpi
Answered 2022-02-25 Author has 5 answers

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