Solve the question using a simple MATLAB code and answer each and every sub$-$questions mentioned in attached image. Write a brief executive summary, answer to the all underlined questions and the significant images, add brief comments and write a clear explanation of why we wrote that step and what output we get.

Thank You.

Note: below is the MATLAB code that I got from previous expert but its not satisfactory. In which I got below mentioned error please rectify it$.$

$>>$ project$1$

Arrays have incompatible sizes for this operation.

Error in project$1($line $88)$

norm$\_$diff$($i$)=$ norm$($coefficients $-$ mean$($data$($:$,($i$-1)*3+1$:i$*3),2))/$ norm$($coefficients$)$;

Write more explanations and what outputs we got.

$\%$ Project $1$

$\%$ Step $1$: Read, convert to black and white, resize images

om$1=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Myobama$1.$jpg$\text{'}))),[12080])$;

om$2=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Myobama$2.$jpg$\text{'}))),[12080])$;

om$3=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Myobama$3.$jpg$\text{'}))),[12080])$;

c$1=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Clooney$1.$jpg$\text{'}))),[12080])$;

c$2=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Clooney$2.$jpg$\text{'}))),[12080])$;

c$3=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Clooney$3.$jpg$\text{'}))),[12080])$;

t$1=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Thatcher$1.$jpg$\text{'}))),[12080])$;

t$2=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Thatcher$2.$jpg$\text{'}))),[12080])$;

t$3=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$Thatcher$3.$jpg$\text{'}))),[12080])$;

$\%$ Step $2$: Reshape images to vectors

om$1\_$vec $=$ reshape$($om$1,[],1)$;

om$2\_$vec $=$ reshape$($om$2,[],1)$;

om$3\_$vec $=$ reshape$($om$3,[],1)$;

c$1\_$vec $=$ reshape$($c$1,[],1)$;

c$2\_$vec $=$ reshape$($c$2,[],1)$;

c$3\_$vec $=$ reshape$($c$3,[],1)$;

t$1\_$vec $=$ reshape$($t$1,[],1)$;

t$2\_$vec $=$ reshape$($t$2,[],1)$;

t$3\_$vec $=$ reshape$($t$3,[],1)$;

$\%$ Step $3$: Calculate average image and average vector

om$\_$ave $=($om$1+$ om$2+$ om$3)/3$;

c$\_$ave $=($c$1+$ c$2+$ c$3)/3$;

t$\_$ave $=($t$1+$ t$2+$ t$3)/3$;

om$\_$ave$\_$vec $=$ reshape$($om$\_$ave, $[],1)$;

c$\_$ave$\_$vec $=$ reshape$($c$\_$ave, $[],1)$;

t$\_$ave$\_$vec $=$ reshape$($t$\_$ave, $[],1)$;

$\%$ Step $4$: Plot training images

figure;

subplot$(3,3,1)$; pcolor$($flipud$($om$1))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,2)$; pcolor$($flipud$($om$2))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,3)$; pcolor$($flipud$($om$3))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,4)$; pcolor$($flipud$($c$1))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,5)$; pcolor$($flipud$($c$2))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,6)$; pcolor$($flipud$($c$3))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,7)$; pcolor$($flipud$($t$1))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,8)$; pcolor$($flipud$($t$2))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

subplot$(3,3,9)$; pcolor$($flipud$($t$3))$; shading interp; colormap$($gray$)$; set$($gca$,$ 'Xtick', $[],$ 'Ytick', $[])$;

$\%$ Step $5$: Plot average images

figure;

subplot$(1,3,1)$; colormap$($gray$)$;

pcolor$($flipud$($om$\_$ave$))$; shading interp;

subplot$(1,3,2)$; colormap$($gray$)$;

pcolor$($flipud$($c$\_$ave$))$; shading interp;

subplot$(1,3,3)$; colormap$($gray$)$;

pcolor$($flipud$($t$\_$ave$))$; shading interp;

$\%$ Step $6$: Create data matrix

data $=[$c$1\_$vec c$2\_$vec c$3\_$vec t$1\_$vec t$2\_$vec t$3\_$vec om$1\_$vec om$2\_$vec om$3\_$vec$]$;

data$\_$dim $=$ size$($data$)$;

data$\_$rank $=$ rank$($data$)$;

singular$\_$values $=$ svd$($data$)$;

$\%$ Step $7$: Evaluate covariance matrix

cov$\_$mat $=$ cov$($data$\text{'})$;

$\%$ Step $8$: Calculate first $9$ eigenvalues and eigenvectors

$[$eigenvectors$,$ eigenvalues$]=$ eigs$($cov$\_$mat, $9)$;

$\%$ Step $9$: Transform test image into column vector

test$\_$img $=$ imresize$($double$($rgb$2$gray$($imread$(\text{'}$obama$4.$jpg$\text{'}))),[12080])$;

test$\_$img$\_$vec $=$ reshape$($test$\_$img, $[],1)$;

$\%$ Step $10$: Evaluate coefficients of expansion

coefficients $=$ eigenvectors' $*$ test$\_$img$\_$vec;

reconstructed$\_$img$\_$vec $=$ eigenvectors $*$ coefficients;

$\%$ Step $11$: Plot coefficients

figure;

bar$($coefficients$)$;

$\%$ Step $12$: Plot remaining $8$ coefficients

figure;

bar$($coefficients$(2$:end$))$;

$\%$ Step $13$: Plot coefficients of test image

figure;

bar$($coefficients$)$;

$\%$ Step $14$: Calculate normalized difference

norm$\_$diff $=$ zeros$(3,1)$;

for i $=1$:$3$

norm$\_$diff$($i$)=$ norm$($coefficients $-$ mean$($data$($:$,($i$-1)*3+1$:i$*3),2))/$ norm$($coefficients$)$;

end

$\%$ Step $15$: Plot test image and reconstruction

figure;

subplot$(1,2,1)$; imshow$($uint$8($test$\_$img$))$;

title$(\text{'}$Original Test Image'$)$;

subplot$(1,2,2)$; imshow$($uint$8($reshape$($reconstructed$\_$img$\_$vec, $120,80)))$;

title$(\text{'}$Reconstructed Test Image'$)$;

$\%$ Step $16$: Calculate normalized error

normalized$\_$error $=$ zeros$(3,1)$;

for i $=1$:$3$

normalized$\_$error$($i$)=$ norm$($coefficients $-$ mean$($data$($:$,($i$-1)*3+1$:i$*3),2))/$ norm$($mean$($data$($:$,($i$-1)*3+1$:i$*3),2))$