Question

Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5​? ​Why?

a. The matrix must have nothing pivot columns. If A had fewer pivot​ columns, then the equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements​ "A has a pivot position in every​ row" and​ "the columns of A span ​" are logically equivalent.
c. The matrix must have nothing pivot columns.​ Otherwise, the equation A would have a free​ variable, in which case the columns of A would not span .
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent

Answer 1

The answer is "Option B".

Explanation:

In the given choices there is some mistake so, the correct choice can be defined in the attached file. please find it.

In the given question, If the column of
`5 * 7` matrix, and the A span is equal to
`R^5`, and then the value of A has a pivot in each row, that's why in each pivot its position in the different columns of A has the five pivot columns, that's why the choice B is correct.