Video Transcript
True or False: If we have the coefficient matrix of a system of linear equations, we can find the augmented matrix for this system.
For this general system of linear equations, the coefficient matrix looks like this. It’s the matrix consisting of only the coefficients of the variables for our linear equations, whereas the augmented matrix looks like this. It’s the matrix consisting of all of the coefficients, but also the constants as well.
So, if we’ve only been given the coefficient matrix, then we’re missing these constant values. The coefficient matrix will give us all of the coefficients. It would also give us an idea of how many linear equations we’ve got and how many variables we’ve got. But unless we know these values for 𝑏 one, 𝑏 two, up to 𝑏 𝑚, the constants, we wouldn’t be able to put together the augmented matrix. Therefore, this is false.
