Write as a Vector Equality -x+y+z=-2 , -x+5y-15z=-26 , 6x-4y-14z=0

Problem

{[−x+y+z=−2],[−x+5*y−15*z=−26],[6*x−4*y−14*z=0])

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],[6])

3. Extract the coefficients of y from each equation to create the second vector: ([1],[5],[−4])

4. Extract the coefficients of z from each equation to create the third vector: ([1],[−15],[−14])

5. Identify the constants on the right side of the equations to form the result vector: ([−2],[−26],[0])

6. Combine these into a linear combination where the variables x y and z scale their respective coefficient vectors.

Final Answer

x*([−1],[−1],[6])+y*([1],[5],[−4])+z*([1],[−15],[−14])=([−2],[−26],[0])

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