Assertion : | array lll a ^ 2 + X ^ 2 & b - z & a + k b + I & b ^ 2 + X ^ 2 & b - x a - k & b + x & c ^ 2 + X ^ 2 array | = | array ccc x & c & -b -c & x & a b & -a & x array |^ 2 Reason : ∆ c = ∆ n–1 where n is order of determinant, and ∆ c is the determinant of cofactors of ∆.

Assertion : | array lll a ^ 2 + X ^ 2 & b - z & a + k b + I & b ^ 2 + X ^ 2 & b - x a - k…

Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants

Assertion :\[\left|\begin{array}{lll} \mathbf{a}^{2}+\mathrm{X}^{2} & \mathbf{b}-\mathbf{z} & \mathbf{a}+\mathbf{k} \\ \mathbf{b}+\mathbf{I} & \mathbf{b}^{2}+\mathrm{X}^{2} & \mathbf{b}-\mathbf{x} \\ \mathbf{a}-\mathbf{k} & \mathbf{b}+\mathbf{x} & \mathrm{c}^{2}+\mathrm{X}^{2} \end{array}\right|\]=\[\left|\begin{array}{ccc} x & c & -b \\ -c & x & a \\ b & -a & x \end{array}\right|^{2}\]
Reason : ∆^c = ∆^n–1 where n is order of determinant, and ∆^c is the determinant of cofactors of ∆.

If both assertion and reason are correct and reason is the correct explanation of assertion.
If both assertion and reason are true but reason is not the correct explanation of assertion.
If assertion is true but reason is false.
If assertion is false but reason is true.

Answer

(A) If both assertion and reason are correct and reason is the correct explanation of assertion.

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Assertion : | array lll a ^ 2 + X ^ 2 & b - z & a + k b + I & b ^ 2 + X ^ 2 & b - x a - k…

Answer

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