Question: Let x be a unit vector in R n . Partition x as Let X1 X2 %3 X1 y - y*

Let x be a unit vector in Rⁿ. Partition x as

X1 X2 х%3 X1 х

Let

Prove that Q is orthogonal. (This procedure gives a quick method for finding an orthonormal basis for Rn with a prescribed first vector x, a construction that is frequently useful in applications.)

X1 X2 %3 X1 y" - y*

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