$\newcommand{\ones}{\mathbf 1}$

# Matrix inverses

$\left[\begin{array}{cc} 1 & -1 \end{array}\right]$
1. has a left inverse
Incorrect.
2. has a right inverse
Correct!
3. is invertible
Incorrect.

The matrix $\left[ \begin{array}{cc} 1 & -1 \\ -1 & 1 \end{array} \right]$ has a left inverse.
1. True
Incorrect.
2. False
Correct!

$A = \left[\begin{array}{cc}1 & 2 \\ 0 & -1 \end{array}\right]$ its own inverse.
1. True
Correct!
2. False
Incorrect.

If a square matrix $A$ has a left inverse, then it has a right inverse.
1. True
Correct!
2. False
Incorrect.

If a matrix has a left and a right inverse, it must be square.
1. True
Correct!
2. False
Incorrect.

If a matrix has a left inverse, its rows are linearly dependent.
1. True
Incorrect.
2. False
Correct!

If the columns of a matrix are linearly independent, then it is left-invertible.
1. True
Correct!
2. False
Incorrect.

About how long does it take to solve a set of 1000 linear equations in 1000 variables, using a computer with a speed of 5 G Flops/sec?
1. 1000 seconds
Incorrect.
2. 100 seconds
Incorrect.
3. 10 seconds
Incorrect.
4. 1 second
Correct!
5. 0.1 second
Incorrect.
6. 0.01 second
Incorrect.

About how long does it take to solve 10 sets of 1000 linear equations in 1000 variables, with the same coefficient matrix but different right-hand sides, using a computer with a speed of 5 G Flops/sec?
1. 1000 seconds
Incorrect.
2. 100 seconds
Incorrect.
3. 10 seconds
Incorrect.
4. 1 second
Correct!
5. 0.1 second
Incorrect.
6. 0.01 second
Incorrect.

Which of the following are true or accurate statements?