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

Problem

{[x+y+z=4],[4*x−3*y−3*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 to create the first vector: ([1],[4])

3. Extract the coefficients of y to create the second vector: ([1],[−3])

4. Extract the coefficients of z to create the third vector: ([1],[−3])

5. Identify the constants on the right side of the equations to form the result vector: ([4],[2])

6. Combine these into a linear combination where each variable scales its respective coefficient vector.

Final Answer

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

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