Multiply the Matrices [[a,0]][[5,1],[0,5]]

Problem

[[a,0]]*[[5,1],[0,5]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 1×2 and the second matrix is 2×2 Since the number of columns in the first matrix matches the number of rows in the second, multiplication is defined. The resulting matrix will be 1×2

2. Calculate the first element of the resulting matrix by taking the dot product of the row of the first matrix and the first column of the second matrix.

a(5)+0*(0)=5*a

3. Calculate the second element of the resulting matrix by taking the dot product of the row of the first matrix and the second column of the second matrix.

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

4. Combine the results into a single row matrix.

[[5*a,a]]

Final Answer

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

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