Question
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Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Determinant and Column Operations:
- The determinant of a matrix is a scalar value representing area, volume, or invertibility.
- Column operations like
can simplify a determinant. - If one column (or row) becomes a linear combination of others or zero, the determinant becomes 0.
is a cube root of unity with identity: .
Calculation:
Let
⇒ Apply column operation:
⇒ First column becomes:
⇒ Using identity:
⇒ First column becomes:
⇒ New matrix:
⇒ Since first column is all zero,
∴ Determinant I = 0
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