$1.(10$ pts$)$ Write a script that reads in the matrices from $$Homework $1$ data.xlsx$$

Here is a good MATLAB command to use:

A$1=$ readmatrix$(\text{'}$Homework $1$ data.xlsx$\text{'},$'Range',$\text{'}$a$3$:c$5\text{'})$

$2.(40$ pts$)$ Do the following MATLAB matrix operations using only $$for$$ loops $($meaning $-$ no usage of MATLAB$$s colon $$:$$ to index through matrices$)$

a$.$ Multiply: Prob$2$a $=$ A$1*$A$2$

b$.$ Multiply: Prob$2$b $=$ C$1*$C$2$

c$.$ Transpose: Prob$2$c $=$ C$1$

d$.$ Element$-$by$-$Element Square: Prob$2$d $=$ B$1.^2$

e$.$ Matrix Exponential: Prob$2$e $=$ exp$($C$1)$

$3.(20$ pts$)$ Subtract your $$looped$$ solution from MATLAB$$s built$-$in command solution for each case. Use MATLAB$$s $$norm$$ command to compute a scalar that is measure of the difference between the $$looped$$ and $$MATLAB$$ solutions.

$4.(20$ pts$)$ Use MATLAB$$s $$tic$$ and $$toc$$ commands to measure execution time so you can see how your $$looped$$ solution time compares with the MATLAB built$-$in command time. Suggest typing in $$help tic$$ in the MATLAB command window to see a good example of how to use the command.

$5.(10$ pts$)$ Use MATLAB$$s $$disp$$ and $$sprintf$$ commands to create a formatted table output for the norm and timing calculations. Output should look somewhat like the following:

MATLAB LOOPS Time Ratio

Solution norm time$($s$)$ time$($s$)$ LOOPS:MATLAB

$-----------------------------------------------------------$

a $|0\mathrm{.}0$e$+000\mathrm{.}00007410\mathrm{.}00061288\mathrm{.}27$

b $|7\mathrm{.}2$e$-140\mathrm{.}00002650\mathrm{.}000625023\mathrm{.}58$

c $|0\mathrm{.}0$e$+000\mathrm{.}00006750\mathrm{.}00033444\mathrm{.}95$

d $|0\mathrm{.}0$e$+000\mathrm{.}00008600\mathrm{.}004785755\mathrm{.}65$

e $|0\mathrm{.}0$e$+000\mathrm{.}00010600\mathrm{.}00049884\mathrm{.}71$