Write as a Vector Equality a=1/2b+2 , a-4b=-12

Problem

{[a=1/2*b+2],[a−4*b=−12])

Solution

1. Rearrange the first equation into standard form A*a+B*b=C by subtracting 1/2*b from both sides.

a−1/2*b=2

2. Identify the coefficients of the variables a and b from both equations to form the vector components.

Equation 1: *1*a−1/2*b=2

Equation 2: *1*a−4*b=−12

3. Construct the vector equality by grouping the coefficients of a into one vector, the coefficients of b into another vector, and the constants into a resultant vector.

a*([1],[1])+b*([−1/2],[−4])=([2],[−12])

Final Answer

a*([1],[1])+b*([−1/2],[−4])=([2],[−12])

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