Determinants

Let A=\begin{bmatrix} 3 & -4\\ 1 & -1 \end{bmatrix} if det. (A+A^2+A^3......A^n)=64, then what is the value of n???

3 Answers

1
" ____________ ·

value of n is 63 since determinant of each of the matrix comes out to be 1

1
" ____________ ·

\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} = A

1
" ____________ ·

Determinant of A has a value of ---1
value of A^2 has a value of --1
similarly A ^3 ---- 1
thus TO HAVE A VALUE OF 64
n must be a value of 63

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