Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\Delta\) = \[ \begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix} \] and x = a + 2p, y = b + 2q, z = c + 2r, then \(\Delta\) equals:</p>
0
\(\Delta\)
2\(\Delta\)
3\(\Delta\)
Step-by-Step Solution
Key Concept: If one row is linear combination of others \to determinant = 0.
1. Third row = $R_1$ + 2 \times $R_2$
2. Rows are linearly dependent
3. Determinant = 0
Correct Answer: 1