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JEE Advanced 2014Paper 1
Exam
JEE Advanced
Year
2014
Paper
Paper 1
Subject
Mathematics
Chapter
Matrices

JEE Advanced 2014 · Paper 1 · Mathematics · Matrices

Let M be a 2 × 2 symmetric matrix with integer entries. Then M is...

Let M be a 2×22 \times 2 symmetric matrix with integer entries. Then M is invertible if

Options

  1. AThe first column of M is the transpose of the second row of M
  2. BThe second row of M is the transpose of the first column of M
  3. CM is a diagonal matrix with non - zero entries in the main diagonal
  4. DThe product of entries in the main diagonal of M is not the square of an integer

Correct answer

C. M is a diagonal matrix with non - zero entries in the main diagonal

Step-by-step solution

Let M=M =\left[{accb\begin{cases}a & c \\ c & b\end{cases}\right](wherea,b,c(where a, b, c\in I)<br>ThenDet) <br >Then DetM = ab - {c}^{2}<br>If<br >Ifa = b = c, Det\left(M\right) = 0<br>If<br >Ifc = 0, a, b \ne 0, Det\left(M\right) \ne 0<br>If<br >Ifab \nesquareofinteger,square of integer,Det\left(M\right) \ne 0
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