Applied Linear Algebra System of Equations MatricesQ1: See the attached image for full question and answer the question. Explanation: It's applied linear algebra question. Create equations for every piece of information given in the question(there are 4 equations) then solve it by using gaussian elimination method.Q2: Calculate the value of “a” for which the system has no solution, exactly one solution or infinitely many solutions.x+2y-3z=43x-y+5z=24x+y+2z=a+2 Q3: Select 3 different digits from these numbers (126789). Use only these numbers as coefficient and create a matrix of 5x5 (with all coefficient non zero) that has rank 3. Also, explain why the rank is equal to 3. Day planningSuppose we have complete freedom over the organisation of our ten-hour day. The options are the following whereHL denotes our happiness level, STB the short term benefit and LTB the long term benefit:OptionPart-time jobHL (per hour) STB (per hour) LTB (per hour)-21Study for university1-14.Play sports/do workout4.1-11a) Suppose on Monday we just require a happiness level equal to +1 (since we enjoyed our weekend), and werequire a total short-term benefit equal to +24 and long-term benefit equal to +15. Can we find a way to schedule theten hours in order to achieve this goal? Justify your answer.1b) Suppose on Wednesday we are tired from a two-day long shift and we need our happiness level to be equal to+13, together with a short-term benefit equal to +8 and long-term benefit equal to +19. Can we find a way toschedule the ten hours in order to achieve this goal? Justify your answer.

PLEASE NOTE THAT AS PER THE BARTLEYBY POLICY I HAVE SOLVED THE FIRST QUESTION FOR ALL THE TWO…

Answered: Suppose we have complete freedom over…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Applied Linear Algebra

System of Equations

Matrices

Q1: See the attached image for full question and answer the question.
Explanation: It's applied linear algebra question. Create equations for every piece of information given in the question(there are 4 equations) then solve it by using gaussian elimination method.

Q2: Calculate the value of “a” for which the system has no solution, exactly one solution or infinitely many solutions.

x+2y-3z=4

3x-y+5z=2

4x+y+2z=a+2

Q3: Select 3 different digits from these numbers (126789). Use only these numbers as coefficient and create a matrix of 5x5 (with all coefficient non zero) that has rank 3.
Also, explain why the rank is equal to 3.