Multiply the Matrices [[1,0],[0,0],[0,1]]*[[-3,4],[5,-2]]

Problem

[[1,0],[0,0],[0,1]]*[[−3,4],[5,−2]]

Solution

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

2. Calculate the first row of the product by multiplying the first row of the first matrix by the columns of the second matrix.

1*(−3)+0*(5)=−3

1*(4)+0*(−2)=4

3. Calculate the second row of the product by multiplying the second row of the first matrix by the columns of the second matrix.

0*(−3)+0*(5)=0

0*(4)+0*(−2)=0

4. Calculate the third row of the product by multiplying the third row of the first matrix by the columns of the second matrix.

0*(−3)+1*(5)=5

0*(4)+1*(−2)=−2

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

Final Answer

[[1,0],[0,0],[0,1]]*[[−3,4],[5,−2]]=[[−3,4],[0,0],[5,−2]]

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