# 5*(3*A-2*B)+Ct  A= 3-2+1 0+1+2 2+0-1 4+5+6 B= 2+1-4 0+3+1 1-2+1 7+10-8 C= 4+1+8 -5+2+0 6-3-9 7+4+11

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember how the matrix and scalar multiplication works, hence if you multiply a matrix by a scalar (number) you need to multiply each element of matrix by this scalar such that:

`3*A = 3*((3,-2,1),(0,1,2),(2,0,-1),(4,5,6)) = ((3*3,-2*3,3*1),(3*0,3*1,3*2),(3*2,3*0,-1*3),(3*4,3*5,3*6))` =`((9,-6,3),(0,3,6),(6,0,-3),(12,15,18))`

`2*B = 2*((2,1,-4),(0,3,1),(1,-2,1),(7,10,-8)) = ((4,2,-8),(0,6,2),(2,-4,2),(14,20,-16))`

You need to perform the difference between the matrices 3A-2B, such that:

`3A-2B = ((9-4,-6-2,3-(-8)),(0-0,3-6,6-2),(6-2,0-(-4),-3-2),(12-14,15-20,18-(-16)))`

`3A-2B = ((5,-8,11),(0,-3,4),(4,4,-5),(-2,-5,34))`

You should come up with the notation 3A-2B=D, hence you need to multiply the matrix D by the scalar 5 such that:

`5D = ((25,-40,55),(0,-15,20),(20,20,-25),(-10,-25,170))`

You need to perform the subtraction of matrices such that:

`5D - C =((25,-40,55),(0,-15,20),(20,20,-25),(-10,-25,170)) -((4,1,8),(-5,2,0),(6,-3,-9),(7,4,11))`

`5D - C = ((21,-41,47),(5,-17,20),(14,23,-16),(-17,-29,159))`

Hence, evaluating the result of subtraction `5D - C`  yields `5D - C = ((21,-41,47),(5,-17,20),(14,23,-16),(-17,-29,159))`  .