Write as a Vector Equality

Problem

{[41*a−4*b+5*c+d=0],[53*a−2*b+7*c+d=0],[25*a+4*b−3*c+d=0])

Solution

1. Identify the variables and their coefficients in each equation of the system.

2. Separate the coefficients of each variable into distinct column vectors.

3. Express the system as a linear combination of these column vectors multiplied by their respective scalars a b c and d

4. Set the resulting vector sum equal to the zero vector.

Final Answer

a*([41],[53],[25])+b*([−4],[−2],[4])+c*([5],[7],[−3])+d*([1],[1],[1])=([0],[0],[0])

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