Write as a Vector Equality x+6y-5z=-7 , 2x-3y+z=-3 , -6x+y+5x=17

Problem

{[x+6*y−5*z=−7],[2*x−3*y+z=−3],[−6*x+y+5*z=17])

Solution

1. Identify the coefficients of the variables x y and z from each equation to form the coefficient matrix A

2. Define the vector of variables x as a column vector containing x y and z

3. Extract the constants from the right-hand side of the equations to form the constant vector b

4. Express the system in the form A*x=b where the matrix-vector product represents the linear combination of the columns.

Final Answer

[[1,6,−5],[2,−3,1],[−6,1,5]]*[[x],[y],[z]]=[[−7],[−3],[17]]

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