# Transpose of a Matrix

Welcome to the matrix transpose calculator, where you'll have the opportunity to learn all about transposing matrices.

#### For Example Addition : Input

$$A + B=\left[ \begin{array}{ccc} 2 & 7 & 0 \\\\ 9 & 12 & 1 \\\\ 3 & 7 & 15 \end{array} \right] + \left[ \begin{array}{ccc} 2 & 1 & 4 \\\\ 5 & 7 & 1 \\\\ 1 & 2 & 5 \end{array} \right]$$

#### Solution

$$\left[ \begin{array}{ccc} \color{Purple}{2} & \color{Crimson}{7} & \color{Chocolate}{0} \\\\ \color{Fuchsia}{9} & \color{DarkMagenta}{12} & \color{Blue}{1} \\\\ \color{OrangeRed}{3} & \color{Chartreuse}{7} & \color{Peru}{15} \end{array} \right] + \left[ \begin{array}{ccc} \color{Purple}{2} & \color{Crimson}{1} & \color{Chocolate}{4} \\\\ \color{Fuchsia}{5} & \color{DarkMagenta}{7} & \color{Blue}{1} \\\\ \color{OrangeRed}{1} & \color{Chartreuse}{2} & \color{Peru}{5} \end{array} \right] =\left[ \begin{array}{ccc}\left(\color{Purple}{2}\right) + \left(\color{Purple}{2}\right) & \left(\color{Crimson}{7}\right) + \left(\color{Crimson}{1}\right) & \left(\color{Chocolate}{0}\right) + \left(\color{Chocolate}{4}\right) \\\\ \left(\color{Fuchsia}{9}\right) + \left(\color{Fuchsia}{5}\right) & \left(\color{DarkMagenta}{12}\right) + \left(\color{DarkMagenta}{7}\right) & \left(\color{Blue}{1}\right) + \left(\color{Blue}{1}\right) \\\\ \left(\color{OrangeRed}{3}\right) + \left(\color{OrangeRed}{1}\right) & \left(\color{Chartreuse}{7}\right) + \left(\color{Chartreuse}{2}\right) & \left(\color{Peru}{15}\right) + \left(\color{Peru}{5}\right) \end{array} \right]$$ $$=\left[ \begin{array}{ccc} 4 & 8 & 4 \\\\ 14 & 19 & 2 \\\\ 4 & 9 & 20 \end{array} \right]$$ For Example answer : $$A + B=\left[ \begin{array}{ccc} 4 & 8 & 4 \\\\ 14 & 19 & 2 \\\\ 4 & 9 & 20 \end{array} \right]$$

#### For Example Subtraction : Input

$$A - B=\left[ \begin{array}{ccc} 2 & 7 & 0 \\\\ 9 & 12 & 1 \\\\ 3 & 7 & 15 \end{array} \right] - \left[ \begin{array}{ccc} 2 & 1 & 4 \\\\ 5 & 7 & 1 \\\\ 1 & 2 & 5 \end{array} \right]$$

#### Solution

$$\left[ \begin{array}{ccc} \color{Chartreuse}{2} & \color{Fuchsia}{7} & \color{Magenta}{0} \\\\ \color{Crimson}{9} & \color{Brown}{12} & \color{Blue}{1} \\\\ \color{Chocolate}{3} & \color{DarkMagenta}{7} & \color{Peru}{15} \end{array} \right] - \left[ \begin{array}{ccc} \color{Chartreuse}{2} & \color{Fuchsia}{1} & \color{Magenta}{4} \\\\ \color{Crimson}{5} & \color{Brown}{7} & \color{Blue}{1} \\\\ \color{Chocolate}{1} & \color{DarkMagenta}{2} & \color{Peru}{5} \end{array} \right] =\left[ \begin{array}{ccc}\left(\color{Chartreuse}{2}\right) - \left(\color{Chartreuse}{2}\right) & \left (\color{Fuchsia}{7}\right) - \left(\color{Fuchsia}{1}\right) & \left(\color{Magenta}{0}\right) - \left(\color{Magenta}{4}\right) \\\\ \left(\color{Crimson}{9}\right) - \left(\color{Crimson}{5}\right) & \left(\color{Brown}{12}\right) - \left(\color{Brown}{7}\right) & \left(\color{Blue}{1}\right) - \left(\color{Blue}{1}\right) \\\\ \left(\color{Chocolate}{3}\right) - \left(\color{Chocolate}{1}\right) & \left(\color{DarkMagenta}{7}\right) - \left(\color{DarkMagenta}{2}\right) & \left(\color{Peru}{15}\right) - \left(\color{Peru}{5}\right) \end{array} \right]$$ $$=\left[ \begin{array}{ccc} 0 & 6 & -4 \\\\ 4 & 5 & 0 \\\\ 2 & 5 & 10 \end{array} \right]$$ For Example answer : $$A - B=\left[ \begin{array}{ccc} 0 & 6 & -4 \\\\ 4 & 5 & 0 \\\\ 2 & 5 & 10 \end{array} \right]$$

#### For Example Multiplication : Input

$$A \cdot B=\left[ \begin{array}{ccc} 2 & 7 & 0 \\\\ 9 & 12 & 1 \\\\ 3 & 7 & 15 \end{array} \right] \cdot \left[ \begin{array}{ccc} 2 & 1 & 4 \\\\ 5 & 7 & 1 \\\\ 1 & 2 & 5 \end{array} \right]$$

#### Solution

$$\left[ \begin{array}{ccc} \color{OrangeRed}{2} & \color{SaddleBrown}{7} & \color{Green}{0} \\\\ \color{Violet}{9} & \color{Red}{12} & \color{Magenta}{1} \\\\ \color{DarkBlue}{3} & \color{DarkCyan}{7} & \color{Blue}{15} \end{array} \right] \cdot \left[ \begin{array}{ccc} \color{OrangeRed}{2} & \color{SaddleBrown}{1} & \color{Green}{4} \\\\ \color{Violet}{5} & \color{Red}{7} & \color{Magenta}{1} \\\\ \color{DarkBlue}{1} & \color{DarkCyan}{2} & \color{Blue}{5} \end{array} \right]=$$ $$=\left[ \begin{array}{ccc}\left(\color{OrangeRed}{2}\right)\cdot\left(\color{OrangeRed}{2}\right)+\left(\color{SaddleBrown}{7} \right)\cdot\left(\color{Violet}{5}\right)+\left(\color{Green}{0}\right)\cdot\left(\color{DarkBlue}{1}\right) & \left(\color{OrangeRed}{2} \right)\cdot\left(\color{SaddleBrown}{1}\right)+\left(\color{SaddleBrown}{7}\right)\cdot\left(\color{Red}{7}\right)+\left(\color{Green}{0} \right)\cdot\left(\color{DarkCyan}{2}\right) & \left(\color{OrangeRed}{2}\right)\cdot\left(\color{Green}{4}\right)+\left(\color{SaddleBrown}{7} \right)\cdot\left(\color{Magenta}{1}\right)+\left(\color{Green}{0}\right)\cdot\left(\color{Blue}{5}\right) \\\\ \left(\color{Violet}{9}\right)\cdot\left(\color{OrangeRed}{2}\right)+\left(\color{Red}{12}\right)\cdot\left(\color{Violet}{5}\right)+\left(\color{Magenta}{1}\right)\cdot\left(\color{DarkBlue} {1}\right) & \left(\color{Violet}{9}\right)\cdot\left(\color{SaddleBrown}{1}\right)+\left(\color{Red}{12}\right)\cdot\left(\color{Red}{7}\right)+\left(\color{Magenta} {1}\right)\cdot\left(\color{DarkCyan}{2}\right) & \left(\color{Violet}{9}\right)\cdot\left(\color{Green}{4}\right)+\left(\color{Red}{12}\right)\cdot\left (\color{Magenta}{1}\right)+\left(\color{Magenta}{1}\right)\cdot\left(\color{Blue}{5}\right) \\\\ \left(\color{DarkBlue}{3}\right)\cdot\left(\color{OrangeRed}{2} \right)+\left(\color{DarkCyan}{7}\right)\cdot\left(\color{Violet}{5}\right)+\left(\color{Blue}{15}\right)\cdot\left(\color{DarkBlue}{1}\right) & \left(\color{DarkBlue}{3}\right)\cdot\left(\color{SaddleBrown}{1}\right)+\left(\color{DarkCyan}{7}\right)\cdot\left(\color{Red}{7}\right)+\left(\color{Blue}{15} \right)\cdot\left(\color{DarkCyan}{2}\right) & \left(\color{DarkBlue}{3}\right)\cdot\left(\color{Green}{4}\right)+\left(\color{DarkCyan}{7} \right)\cdot\left(\color{Magenta}{1}\right)+\left(\color{Blue}{15}\right)\cdot\left(\color{Blue}{5}\right) \end{array} \right]$$ $$=\left[ \begin{array}{ccc} 39 & 51 & 15 \\\\ 79 & 95 & 53 \\\\ 56 & 82 & 94 \end{array} \right]$$ For Example Answer : $$A \cdot B=\left[ \begin{array}{ccc} 39 & 51 & 15 \\\\ 79 & 95 & 53 \\\\ 56 & 82 & 94 \end{array} \right]$$

#### Matrix scalarMultiply operations

Perform the indicated operation for

#### For Example Scalar Multiply : Input

$$2\cdot A=2\left[ \begin{array}{ccc} 2 & 7 & 0 \\\\ 9 & 12 & 1 \\\\ 3 & 7 & 15 \end{array} \right]$$

#### Solution

$$\left[ \begin{array}{ccc} \color{OrangeRed}{2\cdot(2)} & \color{SaddleBrown}{2\cdot(7)} & \color{Green}{2\cdot(0)} \\\\ \color{Violet}{2\cdot(9)} & \color{Red}{2\cdot(12)} & \color{Magenta}{2\cdot(1)} \\\\ \color{DarkBlue}{2\cdot(3)} & \color{DarkCyan}{2\cdot(7)} & \color{Blue}{2\cdot(15)} \end{array} \right]=\left[ \begin{array}{ccc} 4 & 14 & 0 \\\\ 18 & 24 & 2 \\\\ 6 & 14 & 30 \end{array} \right]$$ For Example Answer : $$=\left[ \begin{array}{ccc} 4 & 14 & 0 \\\\ 18 & 24 & 2 \\\\ 6 & 14 & 30 \end{array} \right]$$

#### Matrix scalarDivide operations: Input

$$2\cdot A=2\left[ \begin{array}{ccc} 2 & 7 & 0 \\\\ 9 & 12 & 1 \\\\ 3 & 7 & 15 \end{array} \right]$$

#### Solution

Welcome to the matrix transpose calculator, where you'll have the opportunity to learn all about transposing matrices.

A.