Write as a Vector Equality

Problem

{[x+3*y−3*z−w=11],[4*x+y+2*z+5*w=3],[−3*x−y+z−3*w=−7],[z−y−3*z−5*w=−1])

Solution

1. Identify the variables in the system of linear equations, which are x y z and w

2. Extract the coefficients from each equation to form the column vectors associated with each variable.

3. Represent the system as a linear combination of these column vectors set equal to the vector of constants from the right-hand side of the equations.

4. Simplify the fourth equation if necessary; however, for a standard vector equality, we represent the coefficients as they appear in the system. Note that in the fourth equation, the term z−3*z can be combined to −2*z but we will write the vector based on the provided terms.

Final Answer

x*[[1],[4],[−3],[0]]+y*[[3],[1],[−1],[−1]]+z*[[−3],[2],[1],[−2]]+w*[[−1],[5],[−3],[−5]]=[[11],[3],[−7],[−1]]

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