This statement is false. The system Ax = B is underdetermined when the quantity of unknowns (which are the columns in x) outweighs the number of equations (rows in A). Given A is a 5x7 matrix, it has 5 equations and 7 unknowns. Because B is a 7x1 matrix, it is not underdetermined because there are more equations (7) than unknowns (1). Therefore, the linear system is rather overdetermined.
The statement is b.false. A 5 x 7 matrix times a vector x equals a 5 x 1 vector. The system is usually overdetermined rather than underdetermined.
The statement is false. If A is a 5 x 7 matrix, assuming b is a 5 x 1 matrix (since the product Ax must result in a 5 x 1 matrix, not 7 x 1 as the question incorrectly states), the linear system Ax = b would typically be overdetermined, not underdetermined.
This is because there are more equations (5 rows from matrix A) than there are unknowns (7 columns from matrix A, which represents the number of unknowns in vector x).
For a system to be underdetermined, there would need to be fewer equations than unknowns, which is not the case here. Instead, an underdetermined system would likely arise from a matrix A where its number of rows (equations) is less than its number of columns (unknowns).
