Question 125

If A is a $$4 \times 4$$ matrix and det 2A = 192, then det A =

Solution

Let A be an n × n matrix and c be a scalar then:

det (cA) = $$c^n\ \det\ \left(A\right)$$

det (2A) = $$2^4\ \det\ \left(A\right)$$ = 192

$$\det\ \left(A\right)=\ \frac{192}{2^4}\ =\ \frac{192}{16}\ =\ 12$$

12 Answer

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