If is the adjoint of a 3 × 3 matrix Q and det.(Q) = 4, then c is equal to.

Engineering

Mathematics

Introduction to Determinants

Question

If $P = [\begin{array}{ccc} 1 & c & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{array}]$ is the adjoint of a 3 × 3 matrix Q and det.(Q) = 4, then c is equal to.

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P = adj. Q
⇒ |P| = |adj.Q| = |Q|²
∴ |P| = (4)² ⇒ |P| = 16
$\Rightarrow [\begin{array}{ccc} 1 & c & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{array}] = 16$
⇒ 1(0) – c(– 2) + 3(– 2) = 16 ⇒ 2c = 22
⇒ c = 11.

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