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Title: Row Echelon Form
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Series: Linear Algebra
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Chapter: Matrices and linear systems
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YouTube-Title: Linear Algebra 40 | Row Echelon Form
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Bright video: https://youtu.be/nRXt9zUNLK4
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Dark video: https://youtu.be/kCp7cTwli0M
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la40_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: How many pivots does the following row echelon form have? $$ \left( \begin{array}{cccc}1 & 0 & 3 & 0 \ 0 & 3 & 1 & 0 \ 0 & 0 & 1 & 1 \ \end{array} \right) $$
A1: $3$
A2: $1$
A3: $0$
A4: $2$
A5: $4$
Q2: Is the following matrix in row echelon form? $$ \left( \begin{array}{cccc}1 & 0 & 3 & 0 \ 0 & 3 & 1 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 1 & 1 \ \end{array} \right) $$
A1: No, the zero-row is not at the bottom of the matrix.
A2: No, we need 5 pivots.
A3: Yes and we have 3 pivots.
A4: Yes, for each row the first non-zero is strictly to the right of the first non-zero entry of the row above.
Q3: What are the free variables for this row echelon form? $$ \left( \begin{array}{cccc}1 & 0 & 3 & 0 \ 0 & 3 & 1 & 0 \ 0 & 0 & 1 & 1 \ 0 & 0 & 0 & 1 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ \end{array} \right) $$
A1: There are none.
A2: All variables are free variables.
A3: $x_1, x_2$
A4: Only $x_1$
A5: Only $x_4$
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Last update: 2024-10
