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Find the determinant of the matrix \(\begin{vmatrix} 2 & 7 & 37\\ 3& 6 & 33\\ 4 & 5 & 29 \end{vmatrix}\)
1. 234
2. 132
3. 83
4. 0
5. None of these

1 Answer

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Best answer
Correct Answer - Option 4 : 0

Concept:

Properties of Determinant of a Matrix:

  • If each entry in any row or column of a determinant is 0, then the value of the determinant is zero.
  • For any square matrix say A, |A| = |AT|.
  • If we interchange any two rows (columns) of a matrix, the determinant is multiplied by -1.
  • If any two rows (columns) of a matrix are same then the value of the determinant is zero.


Calculation:

\(\begin{vmatrix} 2 & 7 & 37\\ 3& 6 & 33\\ 4 & 5 & 29 \end{vmatrix}\)

Apply C2 → 5C2 + C1, we get

\(\begin{vmatrix} 2 & 37 & 37\\ 3& 33 & 33\\ 4 & 29 & 29 \end{vmatrix}\)

As we can see that the second and the third column of the given matrix are equal. 

We know that, if any two rows (columns) of a matrix are same then the value of the determinant is zero.

∴ \(\begin{vmatrix} 2 & 7 & 37\\ 3& 6 & 33\\ 4 & 5 & 29 \end{vmatrix}\) = 0

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