benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / The matrix for projecting onto a certain line ℓ, which passes through the origin, is given by begin{pmatrix} frac{1}{50} & frac{7}{50} frac{7}{50} & frac{49}{50} end{pmatrix}.Find…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The matrix for projecting onto a certain line ℓ,\ell, which passes through the origin, is given by \[\begin{pmatrix} \frac{1}{50} & \frac{7}{50} \\ \frac{7}{50} & \frac{49}{50} \end{pmatrix}.\]Find the direction vector of line ℓ.\ell. Enter your answer in the form $\begin{pmatrix} a \\ b \end{pmatrix},$ where a,a, and bb are integers, a>0,a > 0, and gcd(|a|,|b|)=1.\gcd(|a|,|b|) = 1.
Plain-text mathematical notation (without MathML)
The matrix for projecting onto a certain line ℓ, which passes through the origin, is given by
\[\begin{pmatrix} \frac{1}{50} & \frac{7}{50} \\ \frac{7}{50} & \frac{49}{50} \end{pmatrix}.\]Find the direction vector of line ℓ.  Enter your answer in the form $\begin{pmatrix} a \\ b \end{pmatrix},$ where a, and b are integers, a>0, and gcd(|a|,|b|)=1.
Original LaTeX notation
The matrix for projecting onto a certain line $\ell,$ which passes through the origin, is given by
\[\begin{pmatrix} \frac{1}{50} & \frac{7}{50} \\ \frac{7}{50} & \frac{49}{50} \end{pmatrix}.\]Find the direction vector of line $\ell.$  Enter your answer in the form $\begin{pmatrix} a \\ b \end{pmatrix},$ where $a,$ and $b$ are integers, $a > 0,$ and $\gcd(|a|,|b|) = 1.$

level

Level 3

type

Precalculus

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
eee2f297-b61a-5470-9228-9d60fa28dfd3
task_key
precalculus--test--eee2f297-b61a-5470-9228-9d60fa28dfd3
task_revision_id
1
config / split
precalculus / test

Official source

initial import