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Suppose the factorization below is an SVD of a matrix $A$ , with the entries in $U$ and $V$ rounded to two decimal places.$A=\left[\begin{array}{rrr}{.40} & {-.78} & {.47} \\ {.37} & {-33} & {-.87} \\ {-.84} & {-.52} & {-.16}\end{array}\right]\left[\begin{array}{ccc}{7.10} & {0} & {0} \\ {0} & {3.10} & {0} \\ {0} & {0} & {0}\end{array}\right]$$\times\left[\begin{array}{rrr}{.30} & {-.51} & {-.81} \\ {.76} & {.64} & {-.12} \\ {.58} & {-.58} & {.58}\end{array}\right]$a. What is the rank of $A$ ?b. Use this decomposition of $A,$ with no calculations, to write a basis for $\mathrm{Col} A$ and a basis for Nul $A .[\text { Hint: First }$ write the columns of $V . ]$

Note that $A=U \Sigma V^{T},$ so matrix $V$ in this decomposition is given trasposed,so $v_{3}$ is not last column but last row of given matrix.

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 4

The Singular Value Decomposition

Introduction to Matrices

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