Word Count : 690

---

We are to compute the Singular Value Decomposition (SVD) of the matrix $$ A = \begin{bmatrix} 2 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} $$ manually. SVD of a matrix $A$ is: $$ A = U \Sigma V^T $$ where: * $U$ is a $3 \times 3$ orthogonal matrix, * $\Sigma$ is a $3 \times 2$ diagonal matrix with singular values, * $V$ is a $2 \times 2$ orthogonal matrix. --- ### Step 1: Compute $A^T A$ $$ A^T = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} $$ $$ A^T A = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} _____ ____ __________ ___ __________ _____ __________ ______ _____.
____ ____ ______ ____ _____ _________.
__________ ___ ____ __________ ____ _________ ______ _______ _________ ________ ____.
________ ____ _______ _____ ______ ___ ___ ____ ________ ________ ________.
________ _____ ________ _____ ______ ________ ________ ___ __________ _______ _________ _____.
_________ __________ ______ ___ ___ __________ _______ ________ _____.
______ _____ ________ ____ _________ ___ _______.
________ ______ _____ _________ ____ __________ ___ _________.
_______ ______ ______ __________ ______ ___ ______ ________.
_____ _____ ______ ______ ________ ___.
___ _________ _________ _____ ________ ___ ___.
________ ___ _________ __________ __________ ________ _____ ______ _______ __________.
_______ _______ ____ ______ ______ ____.
_____ ________ __________ __________ ____ _______ ____ __________.
________ ____ _________ ___ ____ ________ _________ ___ _________ ________.
___ _________ _______ __________ _______ ___ __________ ________ _____.
_______ __________ _________ _________ _______ _______ _______ ________ ____ ___ _________ ____.
__________ ____ ____ __________ ______ _______ _____ ________ ________ _________ ___ ___.
__________ ____ _________ ___ __________ _________.
___ _______ ___ ___ ___ _____ ___ _______ ________ ___.
_____ ____ __________ _______ __________ _______ _______ _______ _____ ___ _______ ____.
__________ _____ ___ ____ ____ __________ _____ __________ ___ _________ ___ ______.
________ _______ ____ ______ _________ ____ __________ _________.
______ _______ _________ _______ _________ _____ __________ _____ __________ __________ ____.
___ ________ _______ ______ _________ ____ _______ ____ ______.
____ ______ ________ ________ ____ ___ __________ ___.
______ ______ _____ ____ ____ _______ __________ __________ _____ ___ ______.
___ _________ _____ ___ _______ ______ __________.
___ ______ ____ ______ _______ __________.
_______ _______ ____ _________ _______ _____ ______.
_____ _________ ___ _____ _________ ______ __________ ___ __________ ________ _______ __________.
______ ____ ___ ______ ______ ______ ___ _________.
_______ __________ ___ __________ ___ __________ _____ _________ _______ _______.
___ _____ _______ _____ _____ ___ _____ _______ _______ _____ _________.
_____ _________ _______ ___ ____ ___.
_____ _______ _________ _________ _________ _______.
_________ __________ ____ ____ __________ _______ ___ _______ _______ _________ _________ _____.
________ ______ _________ _________ ________ ___ ________ ______ _____ ____ _______ ______.
_____ ________ ___ __________ __________ _____ ________ _______.
____ ___ ___ ______ ______ ___ _______.
__________ _____ ______ _________ __________ _______ __________.
__________ ______ ____ _________ ________ ________ ______ _________ ______.
______ ______ ____ ___ ____ ___.
_____ _________ _____ __________ _______ _________ ________.
_______ ________ __________ _______ ____ _____.
__________ ___ __________ _________ _____ __________ _________ ____ ___.
______ ______ ___ ______ ______ _________ ______ ___.
______ ___ ___ ________ ____ ___ _____ _________.
__________ ___ _________ _________ ______ _______.
____ _________ _________ ___ _________ _____ _________ __________ _________ __________.
_________ ________ _____ _______ ______ ________ _______ ___ __________ _______ ___.
_____ ____ ______ _____ ____ _________.
_________ ____ ______ _______ ________ _____ _________.
______ __________ _______ _________ ____ ________.
_____ _______ _________ _____ _____ ________ _______ __________ ____ ___ _________ ______.
_______ ____ ___ ______ ___ ___ _________.
_____ ______ _____ __________ ____ _______ ________ ______ ________.
____ ____ ___ _______ ____ _____ ___ ____.
___ ________ _____ _________ ___ ___ _________.
____ ______ _________ __________ _____.
___ _______ ___ ___ _______ _______.
__________ _______ __________ ______ _____ _________ __________ _______ _______ _______ ________.
___ _____ __________ ____ _________ ___ ________ _____ _____ _________ _________ ___.
______ ________ ________ ___ _____ ________ __________ _________ ____.
______ _____ _____ __________ _____ ____ ______ ____ _________ __________ _________.
__________ _______ ____ _____ _________ _________ _____ _____ ___ _____.
__________ _________.
Get Full Answer on WhatsApp