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Matrices and Determinants question

2016 · Shift 1 · Q33
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  2. /JEE Advanced
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  4. /Matrices and Determinants
  5. /2016 · Shift 1 · Q33

Matrices and Determinants question

2016 · Shift 1 · Q33

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+4 / −2
Let P=[3−1−220α3−50]P = \left[ {\begin{matrix} 3 & { - 1} & { - 2} \\ 2 & 0 & \alpha \\ 3 & { - 5} & 0 \\ \end{matrix} } \right]P=​323​−10−5​−2α0​​, where α∈\alpha\inα∈ R. Suppose Q=[qij]Q = [{q_{ij}}]Q=[qij​] is a matrix such that PQ = kl, where k ∈\in∈ R, k eee 0 and I is the identity matrix of order 3. If q23=−k8{q_{23}} = - {k \over 8}q23​=−8k​ and det⁡(Q)=k22\det (Q) = {{{k^2}} \over 2}det(Q)=2k2​, then
  1. A
    α\alphaα = 0, k = 8
  2. B
    4α−k+8=04\alpha - k + 8 = 04α−k+8=0
  3. C
    det⁡(Padj(Q))=29\det (Padj(Q)) = {2^9}det(Padj(Q))=29
  4. D
    det⁡(Qadj(P))=213\det (Qadj(P)) = {2^{13}}det(Qadj(P))=213
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