Write as a Vector Equality

Problem

{[x+y+z=116000],[0.08*x+0.06*y+0.09*z=9000],[0.08*x=4*(0.06*y)])

Solution

1. Rearrange the third equation into standard form by moving all variables to the left side.

0.08*x−0.24*y+0*z=0

2. Identify the coefficients of the variables x y and z for each equation to form the coefficient matrix A

A=[[1,1,1],[0.08,0.06,0.09],[0.08,−0.24,0]]

3. Define the variable vector x and the constant vector b from the right-hand side values.

x=[[x],[y],[z]]

b=[[116000],[9000],[0]]

4. Construct the vector equality by expressing the system in the form A*x=b

[[1,1,1],[0.08,0.06,0.09],[0.08,−0.24,0]]*[[x],[y],[z]]=[[116000],[9000],[0]]

Final Answer

[[1,1,1],[0.08,0.06,0.09],[0.08,−0.24,0]]*[[x],[y],[z]]=[[116000],[9000],[0]]

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