The standard basis for[img=22x19]1803b6ab884114f.png[/img]is an orthonormal basis.

An[img=49x19]1803b6aafbee947.png[/img] matrix A has orthonormal columns if and only if[img=59x23]1803b6ab03fb852.png[/img].

Which of the following statement is false? A: Ais an[img=49x19]1803b6abf33899a.png[/img]matrix.[img=66x23]1803b6abfb9f77f.png[/img]is a QR factorization ofA. The columns ofQform an orthonormal basis for the column space ofA. B: If A=QR, where Q has orthonormal columns, then[img=79x27]1803b6ac036f846.png[/img] C: Ahas a QR factorization, then A must be a square matrix. D: Any matrix can have a QR factorization. E: If a matrix A has a QR factorization, then the ranks of A and Q are the same.