I agree with you. From the given information, we can't say that b - a ≠ 0.pyroknife said:
I, II represent rows 1 and 2, respectively.
I am not agreeing with these solutions at step 3 of 5, where they multiply row 2 by 1/(b-a). Correct me if I'm wrong, but we do not know if b-a=0, so I do not think we can divide row II by (b-a) because of the potential of dividing by 0?
What do you guys think?
A linear combination is a mathematical operation that involves multiplying a set of numbers by coefficients and then adding them together. The coefficients can be any real numbers and the numbers being multiplied are typically variables or constants.
Linear combinations are used in science to represent the relationship between variables in a system. They can be used to model physical phenomena, such as chemical reactions or fluid dynamics, and to analyze data in fields such as biology or economics.
There can be multiple solutions for a linear combination because the coefficients used in the operation can vary, resulting in different combinations of the numbers being multiplied. Additionally, some systems may have infinite solutions, meaning that any value for the coefficients will result in a valid solution.
If a linear combination has no solution, it means that the system of equations being modeled is inconsistent or contradictory. This can occur when there are not enough equations to uniquely determine the values of the variables, or when the equations are incompatible with each other.
To determine if a set of solutions for a linear combination is correct, one can substitute the values into the original equations and see if they satisfy all of the equations. If the solutions do not satisfy all of the equations, then they are not valid solutions for the linear combination.