Multiply the Matrices

Problem

[[5,4,2],[3,9,96],[5,12,3]]*[[8,5],[9,9],[5,5]]

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 the columns of the right matrix.

(R_1)*(C_1)=(5×8)+(4×9)+(2×5)=40+36+10=86

(R_1)*(C_2)=(5×5)+(4×9)+(2×5)=25+36+10=71

3. Calculate the elements of the second row.

(R_2)*(C_1)=(3×8)+(9×9)+(96×5)=24+81+480=585

(R_2)*(C_2)=(3×5)+(9×9)+(96×5)=15+81+480=576

4. Calculate the elements of the third row.

(R_3)*(C_1)=(5×8)+(12×9)+(3×5)=40+108+15=163

(R_3)*(C_2)=(5×5)+(12×9)+(3×5)=25+108+15=148

5. Assemble the results into the final 3×2 matrix.

Final Answer

[[5,4,2],[3,9,96],[5,12,3]]*[[8,5],[9,9],[5,5]]=[[86,71],[585,576],[163,148]]

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