Write as a Vector Equality

Problem

{[45*a−30*b+2*d=−1],[18*a+17*b−13*d=−18],[9*a−24*b+42*d=23])

Solution

1. Identify the variables and their coefficients from each equation to form the column vectors.

2. Extract the coefficients of a b and d to create three distinct vectors that are scaled by these variables.

3. Group the constants on the right side of the equations into a single resultant vector.

4. Combine these components into a single vector equation where the sum of the scaled coefficient vectors equals the constant vector.

Final Answer

a*[[45],[18],[9]]+b*[[−30],[17],[−24]]+d*[[2],[−13],[42]]=[[−1],[−18],[23]]

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