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QUESTION 3 3.1 Let the vectors w, x, y and z be given by $\begin{pmatrix} 1 \ 1 \ 1 \ 1 \end{pmatrix}$, $x = \begin{pmatrix} 1 \ -2 \ 0 \ 0 \end{pmatrix}$, $y = \begin{pmatrix} 1 \ 0 \ 0 \ 0 \end{pmatrix}$, $z = \begin{pmatrix} 1 \ 1 \ 1 \ -3 \end{pmatrix}$ Find the Moore-Penrose inverse of the matrix A = wx' + yz'. 3.2 Let A be an m x m matrix partitioned as A = $\begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix}$, where A11 is r x r. Show that if rank (A) = rank (A11) = r, then $\begin{bmatrix} A_{11}^{-1} & 0 \\ 0 & 0 \end{bmatrix}$ is a generalized inverse of A. 3.3 Find a generalized inverse of the matrix A = $\begin{bmatrix} 1 & -1 & -1 & -2 \ -2 & 4 & 1 & 3 \ 1 & 1 & 1 & -3 \ 1 & -1 & 4 & 1 \end{bmatrix}$

          QUESTION 3
3.1 Let the vectors w, x, y and z be given by
$\begin{pmatrix} 1 \ 1 \ 1 \ 1 \end{pmatrix}$, $x = \begin{pmatrix} 1 \ -2 \ 0 \ 0 \end{pmatrix}$, $y = \begin{pmatrix} 1 \ 0 \ 0 \ 0 \end{pmatrix}$, $z = \begin{pmatrix} 1 \ 1 \ 1 \ -3 \end{pmatrix}$
Find the Moore-Penrose inverse of the matrix
A = wx' + yz'.
3.2 Let A be an m x m matrix partitioned as
A = $\begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix}$, where A11 is r x r.
Show that if rank (A) = rank (A11) = r, then
$\begin{bmatrix} A_{11}^{-1} & 0 \\ 0 & 0 \end{bmatrix}$
is a generalized inverse of A.
3.3 Find a generalized inverse of the matrix
A = $\begin{bmatrix} 1 & -1 & -1 & -2 \ -2 & 4 & 1 & 3 \ 1 & 1 & 1 & -3 \ 1 & -1 & 4 & 1 \end{bmatrix}$

QUESTION 3
3.1 Let the vectors w, x, y and z be given by
< p m a t r i x >, x =
< p m a t r i x >, y =
< p m a t r i x >, z =
< p m a t r i x >
Find the Moore-Penrose inverse of the matrix
A = wx' + yz'.
3.2 Let A be an m x m matrix partitioned as
A = < b m a t r i x >, where A11 is r x r.
Show that if rank (A) = rank (A11) = r, then
< b m a t r i x >
is a generalized inverse of A.
3.3 Find a generalized inverse of the matrix
A = < b m a t r i x >

Added by Valerie H.

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