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Which one of the following matrices is an elementary matrix?

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Answer (Detailed Solution Below)

Option 2 :
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Detailed Solution

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Concept:

  • Elementary matrix: An elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation
  • An elementary matrix has each diagonal element 1.


Calculation:

Let's check option b,

Let E = 

Apply R1 → R1 – 5R2

We can see that option B converted in to an identity matrix by one elementary operation.

Hence Option B is correct.

Shortcut Method:

We know that an elementary matrix has each diagonal element 1.

Only B has diagonal element is 1. (By Definition)

So, Option B is correct.

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