Write as a Vector Equality

Problem

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

Solution

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

2. Extract the variables into a single column vector ([x],[y],[z])

3. Represent the constants on the right side of the equations as a resultant column vector.

4. Combine the components into a single vector equation where the variables scale their respective coefficient vectors.

Final Answer

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

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