Q6.Consider R2 with the usual inner product. Let T:R2→R2 be an orthogonal transformation given by T(x,y)=(ax+by,cx+dy) for all x,y∈R, and let A be the matrix representation of T with respect to the standard ordered basis. If a=1 and det(A)<0, find b+c+d.
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Q6
3 Aug 2025
Q6.Consider R2 with the usual inner product. Let T:R2→R2 be an orthogonal transformation given by T(x,y)=(ax+by,cx+dy) for all x,y∈R, and let A be the matrix representation of T with respect to the standard ordered basis. If a=1 and det(A)<0, find b+c+d.
