Write as a Vector Equality

Problem

{[−x+y+z=0],[12−250*y+680*z=0],[10−100*x−680=0])

Solution

1. Rearrange the equations into standard form a*x+b*y+c*z=d by moving constant terms to the right side and aligning variables.

−x+y+z=0

0*x−250*y+680*z=−12

−100*x+0*y+0*z=670

2. Identify the coefficient matrix A the variable vector x and the constant vector b from the system.

A=[[−1,1,1],[0,−250,680],[−100,0,0]]

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

b=[[0],[−12],[670]]

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

[[−1,1,1],[0,−250,680],[−100,0,0]]*[[x],[y],[z]]=[[0],[−12],[670]]

Final Answer

[[−1,1,1],[0,−250,680],[−100,0,0]]*[[x],[y],[z]]=[[0],[−12],[670]]

Want more problems? Check here!