Question
Download Solution PDFFind the determinant of the matrix \(\begin{vmatrix} 2 & 7 & 37\\ 3& 6 & 33\\ 4 & 5 & 29 \end{vmatrix}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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