What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) ?(a) Σab(b) (Σab)^2(c) (Σab)^3(d) (Σab)^4This question was posed to me in an interview for job.This key question is from Application of Determinants in portion Determinants of Mathematics – Class 12

What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + b

1.	What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) ?(a) Σab(b) (Σab)^2(c) (Σab)^3(d) (Σab)^4This question was posed to me in an interview for job.This key question is from Application of Determinants in portion Determinants of Mathematics – Class 12
Answer» Right OPTION is (c) (Σab)^3 For explanation: Applying R1 –> R1 + R2 + R3 \(\begin{vmatrix}\SIGMA ab & \Sigma ab & \Sigma ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) This is equal to, = Σab \(\begin{vmatrix}1 & 1 & 1 \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) Applying C1 –> C1 – C2 and C2 –> C2 – C3 = Σab \(\begin{vmatrix}0 & 0 & 1 \\ \Sigma ab & -\Sigma ab & ab + bc \\0 & \Sigma ca & -ab \end {vmatrix}\) = (Σab)^3

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