Write as a Vector Equality 2x-y+z=3 , 2y-z=1

Problem

2*x−y+z=3,2*y−z=1

Solution

1. Identify the system of linear equations and the variables involved, which are x y and z

2. Rewrite each equation as a dot product between a vector of coefficients and the vector of variables ([x],[y],[z])

3. Construct the coefficient matrix A using the coefficients from the left-hand side of the equations.

4. Define the constant vector b using the values from the right-hand side of the equations.

5. Express the system in the form A*v=b where v is the column vector of variables.

Final Answer

([2,−1,1],[0,2,−1])*([x],[y],[z])=([3],[1])

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