## Related questions with answers

Question

Let $S$ be a spanning set for $V$. Show that the vector $\mathbf{u}$ is in $V^{\perp}$ if and only if $\mathbf{u}$ is orthogonal to every vector in $S$.

Solution

VerifiedStep 1

1 of 3Take $V$ a subspace of $\mathbb R^n$ and $S$ a spanning set for $V$.

Take $\textbf{u}\in V^{\bot}$ then we have that $\textbf{u}\cdot\textbf{v}=0$ for every $\textbf{v}\in V$. Since $S$ is a spanning set for $V$ we have that $S\subset V$ and then $\textbf{u}\cdot\textbf{v}=0$ for every $\textbf{v}\in S$.

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Differential Equations and Linear Algebra

2nd Edition•ISBN: 9780131860612 (1 more)Beverly H. West, Hall, Jean Marie McDill, Jerry Farlow2,405 solutions

#### Differential Equations and Linear Algebra

4th Edition•ISBN: 9780134497181 (3 more)C. Henry Edwards, David Calvis, David E. Penney2,531 solutions

#### Differential Equations and Linear Algebra

4th Edition•ISBN: 9780321964670Scott A. Annin, Stephen W. Goode3,457 solutions

#### Linear Algebra and Differential Equations (Custom Edition for University of California, Berkeley)

2nd Edition•ISBN: 9781256873211David C. Lay, Nagle, Saff, Snider2,362 solutions

## More related questions

1/4

1/7