Find the 10x10 Identity Matrix 10

Problem

(I_10)

Solution

1. Identify the definition of an identity matrix. An identity matrix (I_n) is a square n×n matrix where all elements on the main diagonal are 1 and all other elements are 0

2. Determine the dimensions. For n=10 the matrix must have 10 rows and 10 columns.

3. Construct the matrix by placing 1 at each position (a_i,j) where i=j and 0 where i≠j

Final Answer

(I_10)=[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]

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