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Find the value of x, if the given matrix \(\left[ {\begin{array}{*{20}{c}} 1&2&5\\ 2&x&{10}\\ 3&1&{ - 2} \end{array}} \right]\) is singular

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ISRO URSC Technical Assistant Mechanical 13 Nov 2016 Official Paper
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  1. 4
  2. - 4
  3. \(\frac{1}{4}\)
  4. \(- \frac{1}{4}\)

Answer (Detailed Solution Below)

Option 1 : 4
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Detailed Solution

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Concept:

A singular matrix has a determinant value equals to zero.

Calculation:

Since the determinant value of the given singular matrix is zero.

1 × (-2x - 10) - 2 × (-4 - 30) + 5 × (2 - 3x) = 0

-2x - 10 + 68 + 10 - 15x = 0

17x = 68

x = 4

Hence the required value of x is 4.

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