Multiply the Matrices

Problem

[[395/154,255/154,80/77],[50/77,120/77,30/77],[5/7,5/7,10/7]]*[[77],[159],[231]]

Solution

1. Set up the matrix multiplication by multiplying each row of the first matrix by the column vector.

(R_1)=395/154*(77)+255/154*(159)+80/77*(231)

(R_2)=50/77*(77)+120/77*(159)+30/77*(231)

(R_3)=5/7*(77)+5/7*(159)+10/7*(231)

2. Calculate the first row entry by simplifying the fractions and products.

(R_1)=395/2+40545/154+240

(R_1)=197.5+263.279...+240

(R_1)=(30415+40545+36960)/154

(R_1)=107920/154=53960/77=700.779...

Wait, let's re-evaluate (R_1) precisely:

(R_1)=(395⋅77)/154+(255⋅159)/154+(160⋅231)/154

(R_1)=(30415+40545+36960)/154=107920/154=53960/77

3. Calculate the second row entry.

(R_2)=50+19080/77+90

(R_2)=140+19080/77

(R_2)=(10780+19080)/77=29860/77

4. Calculate the third row entry.

(R_3)=5*(11)+795/7+10*(33)

(R_3)=55+795/7+330

(R_3)=385+795/7

(R_3)=(2695+795)/7=3490/7

Final Answer

[[395/154,255/154,80/77],[50/77,120/77,30/77],[5/7,5/7,10/7]]*[[77],[159],[231]]=[[53960/77],[29860/77],[3490/7]]

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