Find the Result of 3 Times the 3x3 Identity Matrix 3

Problem

3⋅(I_3)

Solution

1. Identify the 3×3 identity matrix, denoted as (I_3) which has ones on the main diagonal and zeros elsewhere.

(I_3)=[[1,0,0],[0,1,0],[0,0,1]]

2. Apply scalar multiplication by multiplying every individual element within the matrix by the scalar value 3

3⋅[[1,0,0],[0,1,0],[0,0,1]]=[[3*(1),3*(0),3*(0)],[3*(0),3*(1),3*(0)],[3*(0),3*(0),3*(1)]]

3. Simplify the products to find the resulting matrix.

[[3,0,0],[0,3,0],[0,0,3]]

Final Answer

3⋅(I_3)=[[3,0,0],[0,3,0],[0,0,3]]

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