Write as a Vector Equality

Problem

ƒ=1−0.2625+x/4500+0.75*(y/4500)+(y*(t−x−y))/(4500⋅1800),1−(0.35−x/3375)−y/4500=0

Solution

1. Simplify the scalar constants and fractions in the first expression to isolate the variables x y and t

1−0.2625=0.7375

0.75*(y/4500)=(0.75*y)/4500=y/6000

4500⋅1800=8100000

2. Expand the quadratic term in the expression for ƒ to identify the coefficients for each variable.

(y*(t−x−y))/8100000=(t*y)/8100000−(x*y)/8100000−(y2)/8100000

3. Simplify the second equation to express it as a linear relationship between x and y

1−0.35+x/3375−y/4500=0

0.65+x/3375−y/4500=0

4. Define the vector v and the vector function F to represent the system as a single equality.

v=[[x],[y],[t]]

5. Construct the vector equality by grouping the expression for ƒ and the constraint equation into a single vector format.

Final Answer

[[ƒ],[0]]=[[0.7375+x/4500+y/6000+(y*t−x*y−y2)/8100000],[0.65+x/3375−y/4500]]

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