3. Find the singular value decomposition (SVD) of the matrix $C = \begin{bmatrix} -24 & 0 & -7 \\ -18 & 0 & 26 \end{bmatrix}$. You may use a calculator to perform arithmetic on this problem, but you need to show the steps of computing SVD.
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Step 1: First, we compute $C^T C$: $$C^T C = \begin{bmatrix} -24 & -18 \\ 0 & 0 \\ -7 & 26 \end{bmatrix} \begin{bmatrix} -24 & 0 & -7 \\ -18 & 0 & 26 \end{bmatrix} = \begin{bmatrix} 576+324 & 0 & 168-468 \\ 0 & 0 & 0 \\ 168-468 & 0 & 49+676 \end{bmatrix} = Show more…
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HW13.1. Compute the SVD of a 2x2 matrix Consider a 2x2 matrix A = [2 0] [0 2] Determine the SVD decomposition UXVT of A C = V = Note: In order to be accepted as correct, all entries of the matrices A, U, Z, V, and T must have absolute values smaller than 0.05.
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[M] Compute an SVD of each matrix. Report the final matrix entries accurate to two decimal places. Use the method of Examples 3 and $4 .$ $A=\left[\begin{array}{rrrr}{-18} & {13} & {-4} & {4} \\ {2} & {19} & {-4} & {12} \\ {-14} & {11} & {-12} & {8} \\ {-2} & {21} & {4} & {8}\end{array}\right]$
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[M] Compute an SVD of each matrix. Report the final matrix entries accurate to two decimal places. Use the method of Examples 3 and $4 .$ $A=\left[\begin{array}{rrrrr}{6} & {-8} & {-4} & {5} & {-4} \\ {2} & {7} & {-5} & {-6} & {4} \\ {0} & {-1} & {-8} & {2} & {2} \\ {-1} & {-2} & {4} & {4} & {-8}\end{array}\right]$
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