Consider a matrix B $=[[3,0],[4,0]]$

Assume that B $=$ U$$V$^$T

$1.$ Derive the largest singular value sigma$1$

$2.$ Derive left singular vector u$1$ corresponding to sigma$1$

$3.$ Derive right singular vector v$1$ corresponding to sigma$1$

$4.$ Derive the rank $1$ approximation B$1=$ sigma$1($u$1$v$1^$T$)$