Write as a Vector Equality 2x+y=5z+8w , x=z+2w

Problem

2*x+y=5*z+8*w,x=z+2*w

Solution

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

2. Rearrange both equations so that all variables are on the left side and the constants (which are zero in this case) are on the right side.

2*x+1*y−5*z−8*w=0

1*x+0*y−1*z−2*w=0

3. Express the system as a linear combination of vectors by using the variables as scalars multiplying their respective coefficient vectors.

x*([2],[1])+y*([1],[0])+z*([−5],[−1])+w*([−8],[−2])=([0],[0])

Final Answer

x*([2],[1])+y*([1],[0])+z*([−5],[−1])+w*([−8],[−2])=([0],[0])

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