Solve the matrices, Linear Algebra homework help

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Mathematics

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PLEASE ANSWER THE THREE QUESTIONS, THANK YOU

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Problem 1 Given the following system of equations: 3x + 2y − 5z = 1 4x − y + z = 0 x−z =2 find all solutions using Gauss-Jordan elimination procedure. Is this an example of consistent system? Why? Problem 2 Find the rank of the following matrix   −1 3 8 −2 1 −1 3 9 −1 3     1 −3 −9 1 −3 0 0 0 0 2 Problem 3 In a certain sense, the following system is not linear: 2 sin α − cos β + 3 tan γ = 3 4 sin α + 2 cos β − 2 tan γ = 10 6 sin α − 3 cos β + tan γ = 9. However, there is still a way to do Gauss-Jordan elimination on it. Does a solution exist for α, β, and γ? 1
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