Video Transcript
True or False: The coefficient matrix has fewer columns than the augmented matrix.
Letโs begin this question by reminding ourselves what the coefficient matrix and the augmented matrix are. They refer to a system of linear equations, such as this general system of linear equations in the variables ๐ฅ one, ๐ฅ two, up two ๐ฅ ๐ and coefficients ๐ ๐๐. These are the coefficients. These are the variables. And these are the constants. Then the coefficient matrix consists of all the coefficients. The coefficient matrix therefore contains the same number of rows as the number of equations and the same number of columns as the number of variables.
The augmented matrix, however, is a little bit different. This too consists of all of the coefficients in the system of linear equations and also has the same number of rows as the number of equations. However, itโs different in that it also contains the constants, therefore giving it an extra column than the coefficient matrix. The augmented matrix, therefore, has the same number of columns as the number of variables plus one extra column for the constants, therefore making it have more columns than the coefficient matrix. So the coefficient matrix has fewer columns than the augmented matrix. This is true.
