Linear Algebra NN.9

1a

A is invertible.

2a

A is row-equivalent to I.

3a

Ax→=0 has only the trivial solution.

4a

The columns of A form a linearly independent set.

5a

The columns of A span Rn.

6a

The linear transformation A maps Rn onto Rn.

7a

There exists an n by n matrix C such that C A = I.

8a

There exists an n by n matrix D such that A D = I

1t

At is invertible.

2t

At is row-equivalent to I.

3t

Atx→=0 has only the trivial solution.

4t

The columns of At form a linearly independent set.

5t

The columns of At span Rn.

6t

The linear transformation At maps Rn onto Rn.

7t

There exists an n by n matrix C such that C At = I.

8t

There exists an n by n matrix D such that At D = I.