Matrices & Determinants
Properties of determinants
Grade Class 12
Question:
The determinant <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
(A) x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup>
(B) x - y
(C) x - y - z
(D) x + y + z
Step-by-Step Solution
Key Concept: Use properties of determinants to simplify the expression by performing row or column operations, then factorize the resulting determinant.
Let D = |x^2 (y+z)^2 yz; y^2 (z+x)^2 zx; z^2 (x+y)^2 xy|. Performing operations R1 -> R1 - R2 and R2 -> R2 - R3, we can factor out (x-y) and (y-z). Further simplification reveals factors like (x+y+z) and (x^2+y^2+z^2).
Correct Answer: 1, 2, 4