Given-that-det-a-b-c-d-e-f-g-h-i-n-find-det-d-2a-e-2b-f-2c-2a-2b-2c-4g-4h-4i-

Question Number 210080 by Spillover last updated on 30/Jul/24

G i v e n t h a t d e t [\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}] = n

f i n d d e t [\begin{matrix} d + 2 a & e + 2 b & f + 2 c \\ 2 a & 2 b & 2 c \\ 4 g & 4 h & 4 i \end{matrix}]

Commented by Frix last updated on 30/Jul/24

{Doesn}^{'} t give any “ {nice}^{″} result .

Commented by Spillover last updated on 30/Jul/24

w h a t r e s u l t d i d y o u g e t ?

Commented by Frix last updated on 30/Jul/24

Sorry I had a typo in my calculation .

The 2^{nd} \det = - 8 n

Commented by Spillover last updated on 30/Jul/24

c o r r e c t

Answered by Spillover last updated on 30/Jul/24

d e t [\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}] = n

d e t [\begin{matrix} a & b & c \\ d & e & f \\ 4 g & 4 h & 4 i \end{matrix}] = 4 n

d e t [\begin{matrix} 2 a & 2 b & 2 c \\ d & e & f \\ 4 g & 4 h & 4 i \end{matrix}] = 8 n

d e t [\begin{matrix} 2 a & 2 b & 2 c \\ d + 2 a & e + 2 b & f + 2 c \\ 4 g & 4 h & 4 i \end{matrix}] = 8 n

d e t [\begin{matrix} 2 a + d & 2 b + e & 2 c + f \\ 2 a & 2 b & 2 c \\ 4 g & 4 h & 4 i \end{matrix}] = - 8 n

Commented by Frix last updated on 30/Jul/24

Yes .

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