Let us consider the inner product space R with its standard inner product. Let T: RR...
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Let us consider the inner product space R" with its standard inner product. Let T: R"R" be defined by T(₁,2,₂)=(x₂ - 1₁, 23-₂₁, 21 — In)- Give an explicit expression for the adjoint T*. Suppose 8 M₂ → P₂(R) is a linear map whose matrix representation with respect to the bases is S= -{[] [] [] []} 01 Use this to compute 3 2 1 2 2 2 10 -2-100 2 1 1 2 and {x²+x+1, 2+1,1} [9] a. Show that a 3 x 3 matrix A = [A₁, A₂, A₁] is invertible if Ã₂ = -4Ã b. Assume that T: R² R² be a transformation given by T(x,y) = (1-xy.x+y). Check if T is a linear transformation. Give a counter example. An x n matrix. A has a set of n linearly independent eigenvectors. Prove that A is diagonalisable. Given H = 2 [10 Marks] 0 21 Determine the characteristic polynomal of matrix H by employing the algorithm for the determination of the eigenvalues of standard Hessenberg matrix. Let us consider the inner product space R" with its standard inner product. Let T: R"R" be defined by T(₁,2,₂)=(x₂ - 1₁, 23-₂₁, 21 — In)- Give an explicit expression for the adjoint T*. Suppose 8 M₂ → P₂(R) is a linear map whose matrix representation with respect to the bases is S= -{[] [] [] []} 01 Use this to compute 3 2 1 2 2 2 10 -2-100 2 1 1 2 and {x²+x+1, 2+1,1} [9] a. Show that a 3 x 3 matrix A = [A₁, A₂, A₁] is invertible if Ã₂ = -4Ã b. Assume that T: R² R² be a transformation given by T(x,y) = (1-xy.x+y). Check if T is a linear transformation. Give a counter example. An x n matrix. A has a set of n linearly independent eigenvectors. Prove that A is diagonalisable. Given H = 2 [10 Marks] 0 21 Determine the characteristic polynomal of matrix H by employing the algorithm for the determination of the eigenvalues of standard Hessenberg matrix.
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The adjoint of the operator 7 is given via the following matrix 7 1 1 1 1 This may be verified by using using the subsequent identification 7x y x 7y for all vectors x and y in R2 To see this we can a... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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