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Q4a) Find the QR factorization 0 the matrixb) Test using the spectral method or suitable matrix norms the guaranteed convergence of Gauss Jacobi method for the foll...

Question

Q4a) Find the QR factorization 0 the matrixb) Test using the spectral method or suitable matrix norms the guaranteed convergence of Gauss Jacobi method for the following system Lx + 42 = 8 4y + 23 = 9 4r + 2y 27 = 10

Q4a) Find the QR factorization 0 the matrix b) Test using the spectral method or suitable matrix norms the guaranteed convergence of Gauss Jacobi method for the following system Lx + 42 = 8 4y + 23 = 9 4r + 2y 27 = 10



Answers

Find the eigenvalues and the corresponding eigenspaces of the stated matrix operator on $R^{3}$. Refer to the tables in Section 4.9 and use geometric reasoning to find the answers. No computations are needed. (a) Reflection about the $x z$ -plane. (b) Orthogonal projection onto the $y z$ -plane. (c) Counterclockwise rotation about the positive $y$ -axis through an angle of $180^{\circ} .$ (d) Dilation with factor $k(k>1)$


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