Write as a Vector Equality y-3z=-12 , -2x+y+2z=5 , 2x+3z=7

Problem

{[y−3*z=−12],[−2*x+y+2*z=5],[2*x+3*z=7])

Solution

1. Identify the coefficients for each variable x y and z in every equation, ensuring that missing variables are treated as having a coefficient of 0

2. Align the variables into a system of linear equations:

0*x+1*y−3*z=−12

−2*x+1*y+2*z=5

2*x+0*y+3*z=7

3. Extract the coefficients into a coefficient matrix A the variables into a vector x and the constants into a vector b

4. Form the vector equality by expressing the system in the form A*x=b or as a linear combination of vectors.

Final Answer

[[0,1,−3],[−2,1,2],[2,0,3]]*[[x],[y],[z]]=[[−12],[5],[7]]

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