Question

1.1. Let R be the counterclockwise rotation by 90 degrees. Vectors r1=[3,3] and r2=[−2,3] are not perpendicular. The inverse U of the matrix M=[r1,r2] has columns perpendicular to r2 and r1, so it must be of the form U=[x⋅R(r2),y⋅R(r1)]^T for some scalars x and y. Find y^−1.

1.2. Vectors r1=[1,1] and r2=[−5,5] are perpendicular. The inverse U of the matrix M=[r1,r2] has columns perpendicular to r2 and r1, so it must be of the form U=[x⋅r1,y⋅r2]^T for some scalars x and y. Find x^−1.

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