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MATH / Find the smallest positive real number C for which

Problem

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problem

Find the smallest positive real number CC for which \[\left\| \begin{pmatrix} 2 & 3 \\ 0 & -2 \end{pmatrix} \bold{v} \right\| \le C \|\bold{v}\|\]for all two-dimensional vectors $\bold{v}.$ Note that for a two-dimensional vector a,\mathbf{a}, ‖a‖\|\mathbf{a}\| is the magnitude of a.\mathbf{a}.
Plain-text mathematical notation (without MathML)
Find the smallest positive real number C for which
\[\left\| \begin{pmatrix} 2 & 3 \\ 0 & -2 \end{pmatrix} \bold{v} \right\| \le C \|\bold{v}\|\]for all two-dimensional vectors $\bold{v}.$

Note that for a two-dimensional vector a, ‖a‖ is the magnitude of a.
Original LaTeX notation
Find the smallest positive real number $C$ for which
\[\left\| \begin{pmatrix} 2 & 3 \\ 0 & -2 \end{pmatrix} \bold{v} \right\| \le C \|\bold{v}\|\]for all two-dimensional vectors $\bold{v}.$

Note that for a two-dimensional vector $\mathbf{a},$ $\|\mathbf{a}\|$ is the magnitude of $\mathbf{a}.$

level

Level 5

type

Precalculus

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Source and history

task_id
1b826861-70d4-59c2-a09b-e396a8900034
task_key
precalculus--test--1b826861-70d4-59c2-a09b-e396a8900034
task_revision_id
1
config / split
precalculus / test

Official source

initial import