Answer to Question #297501 in Linear Algebra for Hossain

Question

(a) Suppose that a matrix in echelon form has more rows than columns. Show that that the matrix must have at least one zero row.

Hints: To get intuition, try this out with a 3 × 2 matrix first. Can there be more pivots than

columns? Consider the row with the last pivot. What must the next row look like?

(b) Suppose that a matrix in echelon form has more columns than rows. Show that there

must be at least one column which does not contain a pivot.

Hints: To get intuition, try this out with a 2×3 matrix first. Can there be more pivots than rows?