If a,b,c are linearly independent, then [ 2 a + b , 2 b + c , 2 c + a ] [ a , b , c ] = Options: A . &nbsp 9 B . &nbsp 8 C . &nbsp 7 D . &nbsp None

Answer: Option A : A [ 2 a + b , 2 b + c , 2 c + a ] [ a , b , c ] = ∣ ∣ ∣ ∣ 2 1 0 0 2 1 1 0 2 ∣ ∣ ∣ ∣ = 2 ( 4 − 0 ) − 1 ( 0 − 1 ) = 8 + 1 = 9

If a,b,c are linearly independent, then [2a+b, 2b+c, 2c+a][a, b

Question -

If a,b,c are linearly independent, then $\frac{[2 a + b, 2 b + c, 2 c + a]}{[a, b, c]} =$

Options:

A . 9

B . 8

C . 7

D . None

Answer: Option A
:
A

\frac{[2 a + b, 2 b + c, 2 c + a]}{[a, b, c]} = ∣ ∣∣ ∣ \begin{matrix} 2 & 1 & 0 0 & 2 & 1 1 & 0 & 2 \end{matrix} ∣ ∣∣ ∣ = 2 (4 - 0) - 1 (0 - 1) = 8 + 1 = 9

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