MathAlgebraLinear algebraSystems of linear equations

Row operations as matrix multiplication

Theory

What do they do?

Report a typo

Correlate the elementary row operator to what it does to the matrix after multiplication

Match the items from left and right columns
(100001010)\begin{pmatrix} 1 & 0 & 0\\ 0 & 0 & 1\\ 0 & 1 & 0 \end{pmatrix}
(001010100)\begin{pmatrix} 0 & 0 & 1\\ 0 & 1 & 0\\ 1 & 0 & 0 \end{pmatrix}
(500010001)\begin{pmatrix} 5 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix}
(100010011)\begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 1 & 1 \end{pmatrix}
(10001−1001)\begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & -1\\ 0 & 0 & 1 \end{pmatrix}
(100010000.5)\begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 0.5 \end{pmatrix}
swap the second and the third rows
divide the third row by 22
subtract the third row from the second
multiply the first row by 55
swap the first and the third rows
add the second row to the third

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