Let T be an orthogonal operator on ℝ2 and let A be its matrix representation with respect to the standard ordered basis of ℝ2. Which one of the following st

Let T be an orthogonal operator on ℝ2 and let A be its matrix representation with respect to the standard ordered basis of ℝ2. Which one of the following statements is incorrect?ans.T is either rotation or reflection on ℝ2A is an orthogonal matrixdet(A)=± 1T is a translation from ℝ2 to ℝ2 Previous Marked for Review Next

Let A =  a b c d , B =  e f g h ∈ M2,2(R) and define hA, Bi = ae + bf + 2cg + 2dh. (a) Show hA, Bi is an inner product of M2,2(R). (b) Find an orthonormal basis for the subspace U of M2,2(R) spanned by −1 0 1 1 ,  0 1 1 0 .

Let B={v1,v2,v3,v4} be a basis for a vector space V. Then the matrix with respect to B for the linear operator T:V→V defined by T(v1)=v2,T(v2)=v3,T(v3)=v4,T(v4)=v1 isA. symmetric matrixB. orthogonal matrixC. singularD. identity matrix

Let p1 = − 22 22 and p2 =  22 22. If the matrix P is orthogonal, show that the column vectors of the matrix form an orthonormal set. (If the matrix is not orthogonal, enter NOT ORTHOGONAL.)Find p1 · p2

Consider the linear transformation T: Rn → Rn whose matrix A relative to the standard basis is given.A = 4 1 −2 7(a) Find the eigenvalues of A. (Enter your answers from smallest to largest.)(𝜆1, 𝜆2) =  5,6 (b) Find a basis for each of the corresponding eigenspaces.B1  =  ⟨1,1⟩  B2  =  ⟨1,2⟩ (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b).