Write as a Vector Equality -x+y+z=-2 , -x+3y-7z=-16 , 7x-5y-15z=0

Problem

{[−x+y+z=−2],[−x+3*y−7*z=−16],[7*x−5*y−15*z=0])

Solution

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

2. Express the system as a linear combination of constant vectors multiplied by the variables.

3. Construct the vector equality by grouping the coefficients of x into the first vector, the coefficients of y into the second vector, and the coefficients of z into the third vector.

4. Set the sum of these vectors equal to the vector containing the constants from the right-hand side of the equations.

Final Answer

x*[[−1],[−1],[7]]+y*[[1],[3],[−5]]+z*[[1],[−7],[−15]]=[[−2],[−16],[0]]

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