Write as a Vector Equality x-y-2z=-6 , 3x+2y=25 , -4x+y-z=12

Problem

{[x−y−2*z=−6],[3*x+2*y=25],[−4*x+y−z=12])

Solution

1. Identify the coefficients of the variables x y and z for each equation in the system.

2. Construct the coefficient matrix A by placing the coefficients of each equation into rows.

A=[[1,−1,−2],[3,2,0],[−4,1,−1]]

3. Define the vector of variables x and the vector of constants b from the right-hand side of the equations.

x=[[x],[y],[z]]

b=[[−6],[25],[12]]

4. Write the system as a single vector equality in the form A*x=b or as a linear combination of column vectors.

Final Answer

[[1,−1,−2],[3,2,0],[−4,1,−1]]*[[x],[y],[z]]=[[−6],[25],[12]]

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