Write as a Vector Equality

Problem

{[x+3*y−3*z−w=8],[4*x+y+4*z+3*w=1],[−3*x−y+z−5*w=−24],[x−y−3*z−5*w=−12])

Solution

1. Identify the coefficients of each variable x y z and w in the system of linear equations.

2. Express each variable as a scalar multiplying a column vector containing its respective coefficients from each equation.

3. Set the sum of these scaled vectors equal to the constant vector formed by the values on the right side of the equations.

Final Answer

x*[[1],[4],[−3],[1]]+y*[[3],[1],[−1],[−1]]+z*[[−3],[4],[1],[−3]]+w*[[−1],[3],[−5],[−5]]=[[8],[1],[−24],[−12]]

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