Multiply the Matrices [[1,0],[0,1]]*[[-1,0,3],[5,7,2]]

Problem

[[1,0],[0,1]]*[[−1,0,3],[5,7,2]]

Solution

1. Identify the identity matrix. The first matrix is the 2×2 identity matrix, denoted as (I_2)

2. Apply the property of identity multiplication. Multiplying any matrix A by the identity matrix I (where dimensions are compatible) results in the original matrix A

3. Verify the dimensions. The first matrix is 2×2 and the second is 2×3 The resulting matrix will be 2×3

4. Calculate the product. Since I⋅A=A the result is the second matrix.

Final Answer

[[1,0],[0,1]]*[[−1,0,3],[5,7,2]]=[[−1,0,3],[5,7,2]]

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