Multiply the Matrices [[a,c],[b,d]][[e,g],[f,h]]

Problem

[[a,c],[b,d]]*[[e,g],[ƒ,h]]

Solution

1. Identify the dimensions of the matrices, which are both 2×2 resulting in a 2×2 product matrix.

2. Calculate the top-left entry by taking the dot product of the first row of the first matrix and the first column of the second matrix.

a*e+c*ƒ

3. Calculate the top-right entry by taking the dot product of the first row of the first matrix and the second column of the second matrix.

a*g+c*h

4. Calculate the bottom-left entry by taking the dot product of the second row of the first matrix and the first column of the second matrix.

b*e+d(ƒ)

5. Calculate the bottom-right entry by taking the dot product of the second row of the first matrix and the second column of the second matrix.

b*g+d(h)

6. Combine these entries into the final matrix structure.

Final Answer

[[a,c],[b,d]]*[[e,g],[ƒ,h]]=[[a*e+c*ƒ,a*g+c*h],[b*e+d(ƒ),b*g+d(h)]]

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