Suppose a coefficient matrix for a system has pivot columns. Is the system consistent? Why or why not? Choose the correct answ
er below. A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent. B. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent. C. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have columns, could have a row of the form , so the system could be inconsistent. D. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have columns, must have a row of the form , so the system is inconsistent.
A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent.
Step-by-step explanation:
Based on Godel's second incompleteness theorem, a system is considered consistent only when the far-right column of the augmented matrix is not a pivot column.
However, given that every column of the coefficient matrix is a pivot column, then there are no top coefficients in the far-right column of the augmented matrix.
Hence, there is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent.
Plug n the h and j so you get 6-(2-1). Due to PEMDAS you do the parenthesis first then subtract so it become 6-1=5. ( You could use distributive property)
