Consider the following statements:

1. the matrix  is singular.

2. The matrix  is non-singular.

Which of the above statements is/are correct?

  1. 1 only 
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer (Detailed Solution Below)

Option 1 : 1 only 
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Detailed Solution

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Concept:

A square matrix is singular if and only if its determinant is 0, otherwise it is non-singular.

 

Calculation:

1. 

Determinant

= 1(2a - 2b) -2 (a - b) + 1(2ab - 2ab)

= 2a - 2b - 2a + 2b + 0

= 0

So this statement is correct.

 

2. 

Determinant

= c (2a - 2b) - 2c (a - b) + 1 (2ab - 2ab)

= 2ac - 2bc - 2ac + 2bc + 0

= 0

So, this statement is not correct.

Hence, option (1) is correct.

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