Question: QUESTION ES 20 marks (a) Let mezo>-- : Find two vectors, x and y, such that span {x, y) = span {u, v} and x

QUESTION ES 20 marks (a) Let mezo>-- : Find two vectors, x and y, such that span {x, y) = span {u, v} and x is orthogonal to y. Explain why your choice of x and y works. (4 marks) b) Determine the values for a, b and c such that the set below is an orthogonal basis for R' (3 marks) (c) Consider =|0 - ys and- =] (i) Verify that u, v and w is an orthonormal basis for R'. (5 marks) 20192020 (ii) Express the vector, 20212022 as a linear combination of u, v and w. 20232024 (3 marks) (d) Diagonalise 8 with an orthogonal matrix.

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