Problem $4.($Transpose$)$ Write a program called

transposo.py that accepts $m($int$)$ and $n($int$)$ as command$-$line arguments, $mn$ floats from standard input representing the elements of an $mn$ matrix $a,$ and writes to standard output the transpose of $a.$ Recall that the transpose of an $m-$by$-n$ matrix $A$ is an $n-$by$-m$ matrix $B$ such that $B_{ij}=A_{ji},$ where $1,$

$1,1,$

$1,2,1,$

$1,3,3,1,$

$1,4,6,4,1P_n(i,j)P_n(i-1,j-1)+P_n(i-1,j)0in{P}_n(i,0)=P_n(i,i)=1in{P}_{n}1j,$ with $P_n(i,0)=P_n(i,i)=1$ for all $i.$ Write a program called

pascal.$py$ that accepts $n(int)as$ command$-$line argument, and writes $P_{n}to$ standard output$\mathrm{.}0j.$Assignment $3(Mozart$ Waltz Generator$)Problem5.(Pascal\text{'}s$ Triangle$)$ Pascal's triangle $P_{n}is$ a triangular array with $n+1$ rows, each listing the coefficients $of$ the binomial expansion $(x+y{)}^i,$ where $0in.$ For example, $P_{4}is$ the triangular array:

$1,$

$1,1,$

$1,2,1,$

$1,3,3,1,$

$1,4,6,4,1$

The term $P_n(i,j)is$ calculated $as{P}_n(i-1,j-1)+P_n(i-1,j),$ where $0in$ and $1j,$ with $P_n(i,0)=P_n(i,i)=1$ for all $i.$ Write a program called

pascal.$py$ that accepts $n(int)as$ command$-$line argument, and writes $P_{n}to$ standard output$\mathrm{.}0$i and $0j.$Assignment $3(Mozart$ Waltz Generator$)Problem5.(Pascal\text{'}s$ Triangle$)$ Pascal's triangle $P_{n}is$ a triangular array with $n+1$ rows, each listing the coefficients $of$ the binomial expansion $(x+y{)}^i,$ where $0in.$ For example, $P_{4}is$ the triangular array:

$1,$

$1,1,$

$1,2,1,$

$1,3,3,1,$

$1,4,6,4,1$

The term $P_n(i,j)is$ calculated $as{P}_n(i-1,j-1)+P_n(i-1,j),$ where $0in$ and $1j,$ with $P_n(i,0)=P_n(i,i)=1$ for all $i.$ Write a program called

pascal.$py$ that accepts $n(int)as$ command$-$line argument, and writes $P_{n}to$ standard output.