Multiply the Matrices

Problem

[[3,0,0],[0,0,5]]*[[1,0,1],[1,1,1],[0,1,0]]

Solution

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

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

(c_11)=(3)*(1)+(0)*(1)+(0)*(0)=3

(c_12)=(3)*(0)+(0)*(1)+(0)*(1)=0

(c_13)=(3)*(1)+(0)*(1)+(0)*(0)=3

3. Calculate the second row of the product by multiplying the second row of the left matrix by each column of the right matrix.

(c_21)=(0)*(1)+(0)*(1)+(5)*(0)=0

(c_22)=(0)*(0)+(0)*(1)+(5)*(1)=5

(c_23)=(0)*(1)+(0)*(1)+(5)*(0)=0

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

Final Answer

[[3,0,0],[0,0,5]]*[[1,0,1],[1,1,1],[0,1,0]]=[[3,0,3],[0,5,0]]

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