CPI 200
Quiz 6 /  graded
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A =(({{0, -1}, {3, 2}})),  v=(({{2}, {2}}))

1.  Find det A

2. Find (v^T)Av

aa= {{0,-1},{3,2}};
v={2,2};
Print[MatrixForm[v.aa.v]];

3. Ax=v is a 2x2 system. The geometry of this system is illustrated as the intersection of two straight lines. Sketch those.

(*
-y  = 2,
3x +2y= 2
*)
Plot[{1 - 1.5x,-2},{x,0,2},PlotStyle->Thick]
LinearSolve[aa,v]

4.  Find a matrix B such that AB ≠ BA

bb={{1,1},{-1,1}};
Print[MatrixForm[aa.bb],MatrixForm[bb.aa]]

5. Find (A^T)A.

Print[MatrixForm[Transpose[aa].aa]]

6. Let C=(({{-1, 0}, {0, 4}})). Find (C^(-1))

cc={{-1,0},{0,4}};
Print[MatrixForm[Inverse[cc]]]

7. Find a 2x2 matrix which reflects all 2D vectors across the x-axis.

pp={{1,0},{0,-1}};
Print[MatrixForm[pp]]

8. What are A’s eigenvalues?