Write as a Vector Equality 5x-4y-6z=-3 , x-3y+z=-1 , -3x-6y+7z=1

Problem

{[5*x−4*y−6*z=−3],[x−3*y+z=−1],[−3*x−6*y+7*z=1])

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 as a single vector equality by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

Final Answer

[[5,−4,−6],[1,−3,1],[−3,−6,7]]*[[x],[y],[z]]=[[−3],[−1],[1]]

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