(Solved): linear algebra and matrix theory Consider the matrices \[ \begin{array}{ll} A_{1}=\left[\begin{array ...

Consider the matrices \[ \begin{array}{ll} A_{1}=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right] & A_{2}=\left[\begin{array}{ll} 3 & 4 \\ 5 & 6 \end{array}\right] \\ A_{3}=\left[\begin{array}{ll} 2 & 3 \\ 4 & 5 \end{array}\right] & A_{4}=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right] \\ A_{5}=\left[\begin{array}{ll} 2 & 2 \\ 3 & 5 \end{array}\right] & A_{6}=\left[\begin{array}{ll} 1 & 2 \\ 2 & 3 \end{array}\right] \end{array} \] Pare down the set of matrices to obtain a basis for \( \mathbb{R}^{2 \times 2} \) You can type your solution below. Alternatively, you can write your solution on paper. In this case, after you submit this test, you will have 10 minutes to take a picture or scan your solution and upload it on "Unit 2 Test - Part II upload", available at the bottom of the Unit 2 module.