(3) Suppose the factorization below is an SVD of a matrix $A$ with entries in $U$ and $V$ rounded to two decimal places. $$ A=\left[\begin{array}{ccc} .40 & -.78 & .47 \ .37 & -.33 & -.87 -.81 & -.52 & -. 16 \end{array} ight]\left[\begin{array}{ccc} 7.10 & 0 & 0W 0 & 3.10 & 0 0 & 0 & 0 \end{array} ight]\left[\begin{array}{ccc} .30 & -.51 & -.81 \ .76 & .64 & -.12 W .58 & -.58 & .58 \end{array} ight] $$ a) What is the rank of $A$ ? b) Using this decomposition, WITH NO CALCULATIONS, write a bases for $C(A)$ and $N(A)($ the column space and null space of $(A)$. (Hint: First, write out the columns of $V$. Note the $A \mathbf {v}_{i}$ is in the column space of $A$.) c) What is the best rank 1 approximation of $A$ ? What about the best rank 2 approximation? CS. JG. 113