Find the Result of 5 Times the 5x5 Identity Matrix 5

Problem

5⋅(I_5)

Solution

1. Identify the 5×5 identity matrix, denoted as (I_5) which consists of ones along the main diagonal and zeros elsewhere.

(I_5)=([1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1])

2. Apply scalar multiplication by multiplying every individual element within the matrix by the scalar 5

5⋅([1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1])=([5*(1),5*(0),5*(0),5*(0),5*(0)],[5*(0),5*(1),5*(0),5*(0),5*(0)],[5*(0),5*(0),5*(1),5*(0),5*(0)],[5*(0),5*(0),5*(0),5*(1),5*(0)],[5*(0),5*(0),5*(0),5*(0),5*(1)])

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

([5,0,0,0,0],[0,5,0,0,0],[0,0,5,0,0],[0,0,0,5,0],[0,0,0,0,5])

Final Answer

5⋅(I_5)=([5,0,0,0,0],[0,5,0,0,0],[0,0,5,0,0],[0,0,0,5,0],[0,0,0,0,5])

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