1.12 a) {{1,2,3},{0,1,1},{0,0,-1}}.{{1,-1,-1},{0,1,1},{0,0,1}} b) {{1,-1,-1},{0,1,1},{0,0,1}}.{{1,2,3},{0,1,1},{0,0,-1}} 1.14 {{0,2},{0,0}}.{{3,1},{2,0}} - {{0,2},{0,0}}.{{6,3},{2,0}} 1.15 b) {{1,6},{3,5},{4,7}}.{{1,0,0},{0,1,0},{0,0,1}}.{{1,2,3},{-1,2,5}}+4*{{1,0,0},{0,1,0},{0,0,1}}^T d) {{1,6},{3,5},{4,7}}^T*{{1,0,0},{0,1,0},{0,0,1}}^6*{{1,6},{3,5},{4,7}}-1/2*({{1,2,3},{-1,2,5}}*{{1,0,0},{0,1,0},{0,0,1}}^4*{{1,2,3},{-1,2,5}}^T)+{{3,4},{5,6}}^2 e) {{1,0},{0,2}}.{{1,2,3},{-1,2,5}}.{{1,6},{3,5},{4,7}}-{{1,0},{0,2}}.{{3,4},{5,6}}.{{1,6},{3,5},{4,7}} h) 2*{{1,0},{0,2}}.{{1,2,3},{-1,2,5}}.{{1,0,0},{0,1,0},{0,0,1}}.{{1},{2},{-1}}+{{3,4},{5,6}}.{{1,2,3},{-1,2,5}}.{{1},{2},{-1}} s) 4*{{3,4},{5,6}}.{{0,0},{0,0}}-{{0,0,0},{0,0,0}}.{{1,6},{3,5},{4,7}} w) {{1,0},{0,2}}.{{1,6},{3,5},{4,7}}+{{1,6},{3,5},{4,7}}.{{3,4},{5,6}} 1.16 f) Transpose[Transpose[{{1,6},{3,5},{4,7}}]-{{1,2,3},{-1,2,5}}] - ({{1,6},{3,5},{4,7}}-Transpose[{{1,2,3},{-1,2,5}}]) t) 2*{{1,6},{3,5},{4,7}}.Transpose[{{3,4},{5,6}}-{{1,0},{0,2}}] - ({{1,6},{3,5},{4,7}}.(2*Transpose[{{3,4},{5,6}}])-2*{{1,6},{3,5},{4,7}}.Transpose[{{1,0},{0,2}}]) x) Transpose[{{-3,4,5,6}}].(3*Transpose[{{1},{2},{-1}}])-3*Transpose[{{1},{2},{-1}}.{{-3,4,5,6}}] 1.28 c) Determinant[{{2,-5,4,3},{3,-4,7,5},{4,-9,8,5},{-3,2,-5,3}}] 1.30 a) Determinant[{{7,3,4},{1,2,1},{3,0,2}}] f) Determinant[{{1,1,1,1},{1,2,1,2},{1,1,2,3},{1,1,1,4}}] m) Determinant[{{1001,1002,1003,1004},{1002,1003,1001,1002},{1001,1001,1001,999},{1001,1000,998,999}}] 1.33 Eigenvalues[{{1,3,4,12},{1/2,0,0,0},{0,1/4,0,0},{0,0,2/3,0}}] solve -x+3y+4z+12u =0, 1/2x-2y=0, 1/4y-2z=0, z-3u=0