Question

Suppose A is a 5times7 matrix. How many pivot columns must A have if its columns span set of real numbers RSuperscript 5​? ​Why?

Answer 1

Five

Explanation:

Pivot columns are said to be columns where pivot exist and a pivot exist in the first nonzero entry of each row in a matrix that is in a shape resulting from a Gaussian elimination.

Suppose A = 5 × 7 matrix

So; if A columns span set of real numbers R⁵

The number of pivot columns that A must have must be present in each row. In a 5 × 7 matrix ; we have 5 rows and 7 columns . So , since A must be present in each row, then :

The matrix must have five pivot columns and we can infer that about the statements that "A has a pivot position in every row" and "the columns of A spans R⁵" are logically equivalent.