Write as a Vector Equality -4x-y-z=1 , x-4y-4z=21 , x+y-6z=3

Problem

{[−4*x−y−z=1],[x−4*y−4*z=21],[x+y−6*z=3])

Solution

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

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

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

4. Extract the coefficients of z from each equation to create the third vector: ([−1],[−4],[−6])

5. Identify the constants on the right side of the equations to form the result vector: ([1],[21],[3])

6. Combine these into a single vector equation where the variables scale their respective coefficient vectors.

Final Answer

x*([−4],[1],[1])+y*([−1],[−4],[1])+z*([−1],[−4],[−6])=([1],[21],[3])

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