If A=[ 1 (1/2) 0 1 ] and A64=[ 1 2λ 0 1 ]. Find the value of λ .

Question

If A=[ 1 (1/2) 0 1 ] and A64=[ 1 2λ 0 1 ]. Find the value of λ . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

A=[ 1 (1/2) 0 1 ] ⇒ A2=[ 1 (1/2) 0 1 ][ 1 (1/2) 0 1 ]=[ 1 1 0 1 ] A3=[ 1 1 0 1 ][ 1 (1/2) 0 1 ]=[ 1 (3/2) 0 1 ] Similarly, A64=[ 1 (64/2) 0 1 ] Leftrightarrow A64=[ 1 32 0 1 ] ⇒ 2λ =32=25 ⇒ λ =5

Q. If $A = [10 \frac{1}{2} 1]$ and $A^{64} = [10 2^{λ} 1] .$ Find the value of $λ .$

$A = [10 \frac{1}{2} 1]$
$\Rightarrow A^{2} = [10 \frac{1}{2} 1] [10 \frac{1}{2} 1] = [1011]$
$A^{3} = [1011] [10 \frac{1}{2} 1] = [10 \frac{3}{2} 1]$
Similarly,
$A^{64} = [10 \frac{64}{2} 1]$
$\Leftrightarrow A^{64} = [10321]$
$\Rightarrow 2^{λ} = 32 = 2^{5}$
$\Rightarrow λ = 5$

Q. If A=[10​21​1​] and A64=[10​2λ1​]. Find the value of λ.

A=[10​21​1​] ⇒A2=[10​21​1​][10​21​1​]=[10​11​] A3=[10​11​][10​21​1​]=[10​23​1​] Similarly, A64=[10​264​1​] ⇔A64=[10​321​] ⇒2λ=32=25 ⇒λ=5

Q. If $A = [10 \frac{1}{2} 1]$ and $A^{64} = [10 2^{λ} 1] .$ Find the value of $λ .$

$A = [10 \frac{1}{2} 1]$
$\Rightarrow A^{2} = [10 \frac{1}{2} 1] [10 \frac{1}{2} 1] = [1011]$
$A^{3} = [1011] [10 \frac{1}{2} 1] = [10 \frac{3}{2} 1]$
Similarly,
$A^{64} = [10 \frac{64}{2} 1]$
$\Leftrightarrow A^{64} = [10321]$
$\Rightarrow 2^{λ} = 32 = 2^{5}$
$\Rightarrow λ = 5$