The value of is :

Engineering

Mathematics

Introduction to Determinants

Question

The value of $∣ \begin{array}{ll} 2 + i & 2 - i \\ 1 + i & 1 - i \end{array} ∣$ is :

A complex quantity

real quantity

cannot be determined

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Let $∣ \begin{array}{ll} 2 + i & 2 - i \\ 1 + i & 1 - i \end{array} ∣$
detA = (2 + i)(1 – i) – (2 – i)(1 + i)
= 2 – 2i + i – i2 – (2 + 2i – i – i²)
= 3 – i – (3 + i) = – 2i
⇒ detA = – 2i ⇒ A complex quantity.

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