Choose the correct answer- Let A- 1 sin- 1- -sin- 1 sin- -1 -sin- 1 - where 0 - 2 - thenA- Det A -0B- Det A -2- -C- Det A -2-4D- Det A -2-4-

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Choose the co...

Question

Choose the correct answer.

Let, where 0 ≤ θ≤ 2π, then

A. Det (A) = 0

B. Det (A) ∈ (2, ∞)

C. Det (A) ∈ (2, 4)

D. Det (A)∈ [2, 4]

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Solution

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Let $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & s i n θ & 1 - s i n θ & 1 & s i n θ - 1 & - s i n θ & 1 \end{matrix} ⎤ ⎥ ⎦$ , where $0 \leq θ \leq 2 π$ , then

a) det A=0
b) det $A ϵ (2, \infty)$
c) det $A ϵ (2, 4)$
d) det $A ε [2, 4]$

[A]_{2 \times 2}

[B]_{3 \times 3}

det (A) = 2

det (B) = 3.

det (det (A) \cdot B) + det (det (B) \cdot A)

A, B

C

n \times n

det (A) = 2, det (B) = 3

det (C) = 5

[det (A^{2} B C^{- 1})]

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