A square matrix of order n , A = [ aij ], is called upper triangular if aij = 0 for i > j, that is, all entries below the main diagonal are zero. (Lower triangular matrices are defined similarly and enjoy the same properties you are showing below). If M and N are two upper triangular matrices of order 3, show that (a) MN is upper triangular (b) |M| is the product of its diagonal elements. Note that (a) and (b) hold for any n .

A )  MN will be multiplying Matrix M and Matrix N

hence MN =

B ) |M| is a product of its diagonal elements because  the matrix of M is equal | M | = a1b2c3 from this | M | is a product of its diagonal elements   for an value of n found in the

Step-by-step explanation:

 = M

M is a upper triangle with an order of three ( 3 )

N=

N is also an upper triangle with an order of three ( 3 )

( A )  MN will be multiplying Matrix M and Matrix N

hence MN =

from the product of MN it is clear that MN is also an upper triangle square matrix as well

( B ) |M| is a product of its diagonal elements because  the matrix of M is equal | M | = a1b2c3 from this | M | is a product of its diagonal elements   for an value of n found in the matrix

if you are looking for the unit rate then the answer would be 9 because unit rate is distance divided by time.

step-by-step explanation: