Write as a Vector Equality -x+2y-3z=1 , 2x+z=0 , 3x-4y+4z=2

Problem

{[−x+2*y−3*z=1],[2*x+z=0],[3*x−4*y+4*z=2])

Solution

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

2. Extract the coefficients of x from each equation to create the first vector:

([−1],[2],[3])

3. Extract the coefficients of y from each equation to create the second vector:

([2],[0],[−4])

4. Extract the coefficients of z from each equation to create the third vector:

([−3],[1],[4])

5. Identify the constants on the right side of the equations to form the result vector:

([1],[0],[2])

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

Final Answer

x*([−1],[2],[3])+y*([2],[0],[−4])+z*([−3],[1],[4])=([1],[0],[2])

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