Write as a Vector Equality x+5y-z=10 , -x+7y-z=18 , 5x-4y-2z=-14

Problem

{[x+5*y−z=10],[−x+7*y−z=18],[5*x−4*y−2*z=−14])

Solution

1. Identify the coefficients of the variables x y and z for each equation to form the column vectors.

2. Extract the coefficients of x from each equation to create the first vector: ([1],[−1],[5])

3. Extract the coefficients of y from each equation to create the second vector: ([5],[7],[−4])

4. Extract the coefficients of z from each equation to create the third vector: ([−1],[−1],[−2])

5. Set the linear combination of these vectors equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*([1],[−1],[5])+y*([5],[7],[−4])+z*([−1],[−1],[−2])=([10],[18],[−14])

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