, 6 Let A(x) left( begin array cc 2 1 2 x 1 2 end array ight) in M(2, mathbb R ), quad x in mathbb R Consider the open ball B 1 (A(1)) C in M(2, mathbb R ) mid C A(1) 1 Here, for B M(2, R) we use the Euclidean norm B left(b 11 2 b 12 2 b 21 2 b 22 2 ight) 1 2 (i) Prove that, if then A(x) B(A(1)) A(x) GL(2, R) (ii) Find Is S A 4(1) 4() 2 A 3 2 GL(2, R)

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Question: , 6. Let [A(x)=left(begin{array}{cc} 2 & 1+2 x 1 & 2 end{array} ight) in M(2, mathbb{R}),quad x in mathbb{R}. ] Consider the open

$, 6. Let \[A(x)=\left(\begin{array}{cc} 2 & 1+2 x \\ 1 & 2$

, 6. Let \[A(x)=\left(\begin{array}{cc} 2 & 1+2 x \\ 1 & 2 \end{array} ight) \in M(2, \mathbb{R}),\quad x \in \mathbb{R}. \] Consider the open ball \[B_{1}(A(1)):=\{C \in M(2, \mathbb{R}) \mid\|C-A(1)\|

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