Mid2Sol_3

Mid2Sol_3 - u2 = v2 v2 0 1 | v3 =(v3 u1)u1(v3 u2)u2 = 0 1 1...

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~u 2 = ~v 2 k ~v 2 k = 1 / 2 1 / 2 1 / 2 1 / 2 ~v || 3 =( ~v 3 · ~u 1 ) ~u 1 +( ~v 3 · ~u 2 ) ~u 2 = 0 1 0 1 ~v 3 = ~v 3 ~v || 3 = 1 1 1 1 ~u 3 = ~v 2 k ~v 2 k = 1 / 2 1 / 2 1 / 2 1 / 2 (b) ~v 1 =2 ~u 1 ~v 2 =0 ~u 1 +2 ~u 2 ~v 3 =1 ~u 1 1) ~u 2 ~u 3 The QR decomposition of the given matrix is: 11 1 1 10 111 1 12 = 1 / 21 / 2 1 / 2 1 / 2 1 / 2 1 / 2 1 / / / 2 1 / 2 1 / / 2 20 1 02 1 00 2 (c) The easiest way is to guess a vector ~u 4 = 1 / 2 1 / 2 1 / 2 1 / 2 so that ~u 1 ,~u 2 3 4 form an orthonormal basis for R 4 . Then ~u 4 is an orthonormal basis for V and
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