Algebra Examples

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}]$

Transpose the matrix by moving element $0, 0$ in the original matrix to element $0, 0$ in the transposed matrix.

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}] \to [\begin{array}{c} 1 \end{array}]$

Transpose the matrix by moving element $0, 1$ in the original matrix to element $1, 0$ in the transposed matrix.

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}] \to [\begin{array}{c} 1 \\ 0 \end{array}]$

Transpose the matrix by moving element $0, 2$ in the original matrix to element $2, 0$ in the transposed matrix.

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}] \to [\begin{array}{c} 1 \\ 0 \\ 1 \end{array}]$

Transpose the matrix by moving element $1, 0$ in the original matrix to element $0, 1$ in the transposed matrix.

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}] \to [\begin{array}{c} 1 & 1 \\ 0 \\ 1 \end{array}]$

Transpose the matrix by moving element $1, 1$ in the original matrix to element $1, 1$ in the transposed matrix.

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}] \to [\begin{array}{c} 1 & 1 \\ 0 & 0 \\ 1 \end{array}]$

Transpose the matrix by moving element $1, 2$ in the original matrix to element $2, 1$ in the transposed matrix.

$[\begin{array}{c} 1 & 0 & 1 \\ 1 & 0 & 0 \end{array}] \to [\begin{array}{c} 1 & 1 \\ 0 & 0 \\ 1 & 0 \end{array}]$

Transpose the matrix by turning all rows in original matrix to columns in the transposed matrix.

$[\begin{array}{c} 1 & 1 \\ 0 & 0 \\ 1 & 0 \end{array}]$