Consider the matrix
A = [[a, b, c],[d, e, f],[g, h, i]]
Given the elementary matrix
E_2= [[1, 0, 0],[0, 6, 0],[0, 0, 1]]
- Compute AE_2.
- Multiplying by E_2 on the right applies a "column operation" to A. Describe the column operation associated with E_2.
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We are given that
`A = ((a,b,c),(d,e,f),(g,h,i))`
and that the elementary matrix `E_2 = ((1,0,0),(0,6,0),(0,0,1))`
(an elementary matrix is one that can be reached from the identity matrix of the same dimension by an elementary row operation).
Therefore we calculate that
`AE_2 = ((a,b,c),(d,e,f),(g,h,i))((1,0,0),(0,6,0),(0,0,1)) = ((a,6b,c),(d,6e,f),(g,6h,i))`
Multiplying by the elementary matrix E_2 on the right is equivalent then to the column operation
`C_2 -> 6C_2`
Answer: AE_2 = `((a,6b,c),(d,6e,f),(g,6h,i))` . From this we can then see that multiplying on the right by the elementary matrix E_2 is equivalent to performing the column operation `C_2 -> 6C_2`.
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