Hurkyl said:How do you rearrange it like that with row and column swaps? (P.S. the determinant of the matrix you created is clearly zero, no matter what a and b are)
matt grime said:yes, the now deleted one... at sciencefourms they don't let ordinary users do that for exactly this reason.
A 4x4 determinant is a mathematical concept used to solve systems of linear equations with four variables. It involves organizing the coefficients of the variables into a square matrix and calculating its determinant.
To find a 4x4 determinant, you need to first set up the matrix with the coefficients of the variables. Then, use the rule of Sarrus or the Laplace expansion method to calculate the determinant. This involves multiplying and adding certain elements of the matrix to obtain the final value.
Solving a 4x4 determinant is useful in various fields of science and engineering, such as physics, chemistry, and economics. It allows for the solution of systems of equations with four variables, which can represent complex relationships between different quantities.
Yes, you can solve a 4x4 determinant by hand using the rule of Sarrus or the Laplace expansion method. However, for larger matrices, it can be time-consuming and prone to errors, so it is more efficient to use a calculator or computer program.
Finding a and b is part of the process of solving a 4x4 determinant. The values of a and b are usually unknowns in the system of equations represented by the determinant, and solving for them allows for the determination of the entire solution set.