Consider the following statements: 1. The matrix ( array ccc 1 & 2 & 1 a & 2 a & 1 b & 2 b & 1 array ) is singular. 2. The matrix ( array ccc c & 2 c & 1 a & 2 a & 1 b & 2 b & 1 array ) is non-singular. Which of the above statements is/are correct?

Step-by-step solution

A square matrix is said to be singular if its determinant is zero & non-singular if its determinant is not equal to zero. aligned & | array ccc 1 & 2 & 1 a & 2 a & 1 b & 2 b & 1 array |= | array ccc 1 & 2 & 1 a-b & 2(a-b) & 0 1-b & 2(1-b) & 0 array | & Applying R ₂ R ₂- R ₃ ; R ₃ R ₁- R ₃ & =(a-b)(1-b) | array ccc 1 & 2 & 1 1 & 2 & 0 1 & 2 & 0 array | & =(a-b)(1-b)(2-2)=0 It is singular. aligned aligned & Again, | array lll c & 2 c & 1 a & 2 a & 1 b & 2 b & 1 array |= | array ccc c & 2 c & 1 a-b & 2(a-b) & 0 b-c &