91Ó°ÊÓ

Find \(A^{+}\) and use it to compute the minimal length least squares solution to \(A \mathbf{x}=\mathbf{b}\) $$A=\left[\begin{array}{ll} 1 & 2 \\ 2 & 4 \end{array}\right], \mathbf{b}=\left[\begin{array}{l} 3 \\ 5 \end{array}\right]$$

Compute the pseudoinverse of \(A\) $$A=\left[\begin{array}{l} 1 \\ 2 \end{array}\right]$$

Show that if \(A\) is an invertible matrix, then \(\operatorname{cond}(A) \geq 1\) with respect to any matrix norm.

Show that if \(A\) and \(B\) are invertible matrices, then cond \((A B) \leq \operatorname{cond}(A)\) cond \((B)\) with respect to any matrix norm.

Compute the pseudoinverse of \(A\) $$A=\left[\begin{array}{r} 1 \\ -1 \\ 2 \end{array}\right]$$

Find \(A^{+}\) and use it to compute the minimal length least squares solution to \(A \mathbf{x}=\mathbf{b}\) $$A=\left[\begin{array}{lll} 3 & 0 & 0 \\ 0 & 0 & 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{l} 3 \\ 0 \end{array}\right]$$

Find \(A^{+}\) and use it to compute the minimal length least squares solution to \(A \mathbf{x}=\mathbf{b}\) $$A=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \\ 1 & 1 \end{array}\right], \mathbf{b}=\left[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right]$$

Compute the pseudoinverse of \(A\) $$A=\left[\begin{array}{rr} 1 & 3 \\ -1 & 1 \\ 0 & 2 \end{array}\right]$$

Compute the pseudoinverse of \(A\) $$A=\left[\begin{array}{ll} 1 & 3 \\ 3 & 1 \\ 2 & 2 \end{array}\right]$$

Find \(A^{+}\) and use it to compute the minimal length least squares solution to \(A \mathbf{x}=\mathbf{b}\) $$A=\left[\begin{array}{lll} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{array}\right], \mathbf{b}=\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right]$$