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

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?