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Find the determinant of the matrix 

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  1. abc
  2. xyz
  3. 0
  4. ax + by + cz

Answer (Detailed Solution Below)

Option 3 : 0
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Detailed Solution

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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:

Apply R1 → R1 + R2

= 

As we can see that the first and the third row 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.

 = 0

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