Convert the following matrix from a Dense to a Sparse representation:

$$

$$

$$

$$

$$

$$

$$

$$

$102113000$

$0211310500$

$1044530090$

$0211357010$

$1002172010$

$010000$

$$

$$

$$

$$

$$

$$

$$

$$

$$ Explain the differences between storing a matrix with a Dense or Sparse representa$-$

tion.

$$ Invert the matrix using both dense and sparse representations. Explain the observed

differences in the compute time and memory usage. $($Hint: Most computing languages

offer tools to measure computational speed and memory use. In Julia this is done with

the @time macro