All vectors have length N $=9.($i$)(4$ pts$.)$ The entries of the time$-$domain vector x $(1)=211211211$ T are given by $2$ cos n$,$ where n $=0$ : $8.$ What is the value of $?$ Express x $(1)$ as the sum of two Fourier sinusoids$.$ By considering the appropriate column of the Fourier matrix V$,$ determine and display the DFT X$(1).($ii$)(4$ pts$.)$ Similarly, express the time$-$domain vector x $(2)=011011011$ T as a linear combination of the same two Fourier sinusoids as in part $($i$).$ Hence determine and display the DFT X$(2).($iii$)(4$ pts$.)$ Determine and display the DFT X$(3)$ of x $(3)[$n$]=$ cos$(2$n$/9)+3$ cos$(4$n$/9),$ n $=0,...,8($iv$)(4$ pts$.)$ Determine and display the DFT X$(4)$ of x $(4)[$n$]=$ sin$(8$n$/9),$ n $=0,...,8($v$)(4$ pts$.)$ If the time$-$domain vector x $(5)$ has DFT X$(5)=1809$j $2700279$j $0$ T write an equation for x $(5)[$n$],$ where n $=0$ : $8.$ Your equation should be in terms of cosines and sines.