Find the Result of 4 Times the 4x4 Identity Matrix 4

Problem

4⋅(I_4)

Solution

1. Identify the 4×4 identity matrix, denoted as (I_4) which contains ones along the main diagonal and zeros elsewhere.

(I_4)=[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]

2. Apply scalar multiplication by multiplying every individual element within the matrix by the scalar value 4

4⋅[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]=[[4*(1),4*(0),4*(0),4*(0)],[4*(0),4*(1),4*(0),4*(0)],[4*(0),4*(0),4*(1),4*(0)],[4*(0),4*(0),4*(0),4*(1)]]

3. Simplify the products to obtain the resulting scalar matrix.

[[4,0,0,0],[0,4,0,0],[0,0,4,0],[0,0,0,4]]

Final Answer

4⋅(I_4)=[[4,0,0,0],[0,4,0,0],[0,0,4,0],[0,0,0,4]]

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