Multiply the Matrices [[1,2],[3,2]][[c],[-c]]

Problem

[[1,2],[3,2]]*[[c],[−c]]

Solution

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

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

1*(c)+2*(−c)

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

3*(c)+2*(−c)

4. Simplify the expressions for each entry.

c−2*c=−c

3*c−2*c=c

Final Answer

[[1,2],[3,2]]*[[c],[−c]]=[[−c],[c]]

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