How to do this Matrices Question?

[MathsIsFun]

Prove by Induction that Aⁿ = [2ⁿ 0 ]
[ 1-2ⁿ 1 ]

 

[MathsIsFun]

[ 2ⁿ 0 ]
[ 1-2ⁿ 1 ]

this is a matrix

 

[Ishuda]

Prove by Induction that Aⁿ = [2ⁿ 0 ]
[ 1-2ⁿ 1 ]

So what is
\(\displaystyle \begin{pmatrix}2& 0\\-1& 1\end{pmatrix}\, \, \begin{pmatrix}2^n& 0\\1-2^n& 1\end{pmatrix}\)

 

[stapel]

Prove by Induction that Aⁿ = [2ⁿ 0 ]
[ 1-2ⁿ 1 ]

What is the matrix A? Also, are you familiar with induction proofs? Thank you!

 

[MathsIsFun]

So what is
\(\displaystyle \begin{pmatrix}2& 0\\-1& 1\end{pmatrix}\, \, \begin{pmatrix}2^n& 0\\1-2^n& 1\end{pmatrix}\)

Isnt it:

[4^n........... 0]
[-4^n+1.... 1 ]

 

[Deleted member 4993]

Isnt it:

[4^n........... 0]
[-4^n+1.... 1 ]

No 2 * 2ⁿ = 2ⁿ⁺¹

 

[MathsIsFun]

No 2 * 2ⁿ = 2ⁿ⁺¹

So it actually = [2^n+1 0]
......................[-4^n+1 1]

 

[Ishuda]

So it actually = [2^n+1 0]
......................[-4^n+1 1]

You now have the first row correct but still don't have the second row correct. BTW: You should use grouping symbols, i.e. 2^(n+1), not 2^n+1 which, properly, would be read as (2^n) + 1 although the meaning is clear a lot of times because of context.

 

[MathsIsFun]

You now have the first row correct but still don't have the second row correct. BTW: You should use grouping symbols, i.e. 2^(n+1), not 2^n+1 which, properly, would be read as (2^n) + 1 although the meaning is clear a lot of times because of context.

Is it:

[2^(n+1) 0]
[-4^(n+1) 0]

 

[Deleted member 4993]

Is it:

[2^(n+1) 0]
[ -4^(n+1) 0]

Do you know how multiply matrices or just guessing?! How did you get -4^(n+1) in the second row, first column??