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))