Can you please help me with it thank you **Singular Value Decomposition and Solutions to Linear Systems****Problem 3.17:**Consider a set of algebraic equations \(Mx = b\) where\[M = \begin{bmatrix}1 & -0.778 & -1.222 \\0 & 0.889 & -0.889 \\1 & -0.111 & 2.111\end{bmatrix}\]The singular value decomposition of \(M\) is \(M = USV^*\) where\[U = \begin{bmatrix}-0.540 & 0.613 & 0.577 \\-0.260 & -0.774 & 0.577 \\0.800 & 0.161 & 0.577\end{bmatrix}\]\[S = \begin{bmatrix}2.91 & 0 & 0 \\0 & 1.30 & 0 \\0 & 0 & 0\end{bmatrix}\]\[V = \begin{bmatrix}-0.461 & 0.348 & -0.816 \\0.034 & -0.912 & -0.408 \\0.887 & 0.216 & -0.408\end{bmatrix}\](i) Based on this decomposition, show that if an exact solution to \(Mx = b\) exists, then it will not be unique.(ii) Determine any value for the vector \(b\) such that a solution to \(Mx = b\) will exist.(iii) What is the set of all \(b\) such that a solution to \(Mx = b\) will exist?(iv) For the \(b\) of part (ii), determine a solution to \(Mx = b\).(v) Using the \(b\) of part (ii), determine all solutions to \(Mx = b\). Rather than performing the calculations based on the given numbers, use the notation below to develop a formula for the solution.\[U = [u_1, u_2, u_3] \quad S = \begin{bmatrix} \sigma_1 & 0 & 0 \\ 0 & \sigma_2 & 0 \\ 0 & 0 & 0 \end{bmatrix}

Name: Can you please help me with it thank you **Singular Value Decompositio
Uploaded: 2024-03-20T07:06:27.000Z
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Description: Can you please help me with it thank you **Singular Value Decomposition and Solutions to Linear Systems****Problem 3.17:**Consider a set of algebraic equations \(Mx = b\) where\[M = \begin{bmatrix}1 & -0.778 & -1.222 \\0 & 0.889 & -0.889 \\1 & -0.111