#forall u, v#, #((2,3,5,7), (13,17,19,23)) * ((64,28,-18), (-64,-27,18), (15,5,-5), (0,0,1)) * ((1), (u), (v)) = ((11), (29))# ?

Let, #[A]_(2xx4)=[(2,3,5,7),(13,17,19,23)]#,

#[B]_(4xx3)=[(64,28,-18),(-64,-27,18),(15,5,-5),(0,0,1)]#,

#[C]_(3xx1)=[(1),(u),(v)]#.

Then, #[A]_(2xx4)*[B]_(4xx3)*[C]_(3xx1)# is defined, and, is a

#(2xx1)# Matrix. .

Now, #[B]_(4xx3)*[C]_(3xx1)# is a #4xx1# Matrix, given by,,

#=[(64+28u-18v),(-64-27u+18v),(15+5u-5v),(v)]#.

Next, #[A]_(2xx4)*{[B]_(4xx3)*[C]_(3xx1)}# is a #2xx1# Matrix

and, #[A]_(2xx4)*{[B]_(4xx3)*[C]_(3xx1)}#,

#=[(2,3,5,7),(13,17,19,23)]*[(64+28u-18v),(-64-27u+18v),(15+5u-5v),(v)]#.

Now,

#2(64+28u-18v)+3(-64-27u+18v)+5(15+5u-5v)+7(v),#

#=(128-192+75)+u(56-81+25)+v(-36+54-25+7)#,

#=11#, and,

#13(64+28u-18v)+17(-64-27u+18v)+19(15+5u-5v)+23(v),#

#=(832-1088+285)+u(364-459+95)+v(-234+306-95+23)#,

#=29#.

#:.[(2,3,5,7),(13,17,19,23)]*[(64+28u-18v),(-64-27u+18v),(15+5u-5v),(v)]=[(11),(29)]#.

From here on, consider the variables exchange

#alpha = 3 + u - v#

#beta = u#

#ABC = K#

#ADE = K#

#D = ((10, 18, 10), (-10, -18, -9), (0, 5, 0), (3, -1, 1)), E = ((1), (alpha), (beta))#

#DE = BC#

#E = MC#

#DMC = BC => DM = B => M = ((1, 0, 0), (3, 1, -1), (0, 1, 0))#