JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let for \(i\, = 1, 2, 3, p_i(x)\) be a polynomial of degree \(2\) in \(x, p'_i(x)\) and \(p"_i(x)\) be the first and second order derivatives of \(p_i(x)\) respectively. Let, \(A\left( x \right)=\left[ \begin{matrix}
{{p}_{1}}\left( x \right) & p_{1}^{'}\left( x \right) & p_{1}^{''}\left( x \right) \\
{{p}_{2}}\left( x \right) & p_{2}^{'}\left( x \right) & p_{2}^{''}\left( x \right) \\
{{p}_{3}}\left( x \right) & p_{3}^{'}\left( x \right) & p_{3}^{''}\left( x \right) \\
\end{matrix} \right]\) and \(B(x)\,= [A(x)]^T\) \(A(x)\). Then determinant of \(B(x)\)
- A is a polynomial of degree \(6\) in \(x\)
- B is a polynomial of degree \(3\) in \(x\)
- C is a polynomial of degree \(2\) in \(x\)
- D does not depend on \(x\)
Answer & Solution
Correct Answer
(A) is a polynomial of degree \(6\) in \(x\)
Step-by-step Solution
Detailed explanation
It is clear from the above multiplication, the degree of determinant of \(B(x)\) can not be less than \(4\) . Let \({p_1}x = {a_1}{x^2} + {b_1}x + {c_1}\) \({p_2}x = {a_2}{x^2} + {b_2}x + {c_2}\) and \({p_3}x = {a_3}{x^2} + {b_3}x + {c_3}\) where…
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