1. Using pencil and paper, compute the decomposition of using a Givens rotation that you explicitly build. 2. Using pencil and paper, compute the QR decomposition of using a Householder reflection...

1.

Using pencil and paper, compute the

decomposition of using a Givens rotation that you explicitly build.

2.

Using pencil and paper, compute the QR decomposition of using a Householder reflection that you explicitly build.

3.

Show that in the full

decomposition of the full rank

matrix


the vectors

<sub>n

m</sub>
are an orthonormal basis for the null space of

^T

Hint: Using block matrix notation, write

where

₁
consists of the first

columns of

and the columns of

₂
are the remaining

columns. Write

in block matrix notation also.