Multiply the Matrices

Problem

[[580,840,320],[560,420,160],[860,1020,540]]*[[3.05,0.05],[3.15,0.08],[3.25,0.10]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 3×3 and the second is 3×2 so the resulting matrix will be 3×2

2. Calculate the elements of the first row by multiplying the first row of the left matrix by each column of the right matrix.

(R_1)*(C_1)=580*(3.05)+840*(3.15)+320*(3.25)=1769+2646+1040=5455

(R_1)*(C_2)=580*(0.05)+840*(0.08)+320*(0.10)=29+67.2+32=128.2

3. Calculate the elements of the second row using the same dot product method.

(R_2)*(C_1)=560*(3.05)+420*(3.15)+160*(3.25)=1708+1323+520=3551

(R_2)*(C_2)=560*(0.05)+420*(0.08)+160*(0.10)=28+33.6+16=77.6

4. Calculate the elements of the third row.

(R_3)*(C_1)=860*(3.05)+1020*(3.15)+540*(3.25)=2623+3213+1755=7591

(R_3)*(C_2)=860*(0.05)+1020*(0.08)+540*(0.10)=43+81.6+54=178.6

5. Assemble the calculated values into the final 3×2 matrix.

Final Answer

[[580,840,320],[560,420,160],[860,1020,540]]*[[3.05,0.05],[3.15,0.08],[3.25,0.10]]=[[5455,128.2],[3551,77.6],[7591,178.6]]

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