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MATH / Find the 3×3 matrix M such that

Problem

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problem

Find the 3×33 \times 3 matrix M\mathbf{M} such that \[\mathbf{M} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} y \\ z \\ x + y + z \end{pmatrix}\]for all real numbers x,x, y,y, and z.z.
Plain-text mathematical notation (without MathML)
Find the 3×3 matrix M such that
\[\mathbf{M} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} y \\ z \\ x + y + z \end{pmatrix}\]for all real numbers x, y, and z.
Original LaTeX notation
Find the $3 \times 3$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} y \\ z \\ x + y + z \end{pmatrix}\]for all real numbers $x,$ $y,$ and $z.$

level

Level 2

type

Precalculus

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Source and history

task_id
abe6520e-5474-5d43-ac93-0fa74390583a
task_key
precalculus--test--abe6520e-5474-5d43-ac93-0fa74390583a
task_revision_id
1
config / split
precalculus / test

Official source

initial import