Question

determine the householder transformation that annihilates all but the first entry of the vector [1 1 1 1 ]t. specifically, if (

Answer 1

Answer:

v=a+ 2e1= [3 1 1 1] $x^{T}$.

Step-by-step explanation:

Let a = $^{}$$\left[\begin{array}{ccc}\\1&1&1\\\end{array}\right] ^{T}$and we know that$\alpha$=±║α║₂= 2.

As we have gone over in class, the formula for v is v= a-$\alpha$e1

with the sign of chosen to avoid subtraction. This gives v=a+ 2e1= [3 1 1 1] $x^{T}$.

Disclaimer ;The question is incomplete

Question:

Determine the Householder transformation that annihilates all but the first entry of the vector[1 1 1 1]>Specifically, if

$I-2vv^{T}/v^{T}v\left[\begin{array}{ccc}1\\1\\1\\1\end{array}\right]$==$\left[\begin{array}{ccc}\alpha \\0\\0\\0\end{array}\right]$

what are the values of α and v?

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