Matrix Calculator
Solve matrices step by step
This calculator will add, subtract, multiply, divide, and raise to power two matrices, with steps shown. It will also find the determinant, inverse, rref (reduced row echelon form), null space, rank, eigenvalues, and eigenvectors and will multiply the matrix by a scalar.
Your Input
Calculate $$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 0 & 4\\0 & 1 & 0\end{array}\right] + \left[\begin{array}{ccc}2 & 1 & 4\\5 & 7 & 1\\1 & 2 & 5\end{array}\right].$$$
Solution
$$$\left[\begin{array}{ccc}{\color{DarkBlue}1} & {\color{Chocolate}0} & {\color{Peru}0}\\{\color{SaddleBrown}0} & {\color{Purple}0} & {\color{Chartreuse}4}\\{\color{Blue}0} & {\color{Violet}1} & {\color{Fuchsia}0}\end{array}\right] + \left[\begin{array}{ccc}{\color{DarkBlue}2} & {\color{Chocolate}1} & {\color{Peru}4}\\{\color{SaddleBrown}5} & {\color{Purple}7} & {\color{Chartreuse}1}\\{\color{Blue}1} & {\color{Violet}2} & {\color{Fuchsia}5}\end{array}\right] = \left[\begin{array}{ccc}{\color{DarkBlue}\left(1\right)} + {\color{DarkBlue}\left(2\right)} & {\color{Chocolate}\left(0\right)} + {\color{Chocolate}\left(1\right)} & {\color{Peru}\left(0\right)} + {\color{Peru}\left(4\right)}\\{\color{SaddleBrown}\left(0\right)} + {\color{SaddleBrown}\left(5\right)} & {\color{Purple}\left(0\right)} + {\color{Purple}\left(7\right)} & {\color{Chartreuse}\left(4\right)} + {\color{Chartreuse}\left(1\right)}\\{\color{Blue}\left(0\right)} + {\color{Blue}\left(1\right)} & {\color{Violet}\left(1\right)} + {\color{Violet}\left(2\right)} & {\color{Fuchsia}\left(0\right)} + {\color{Fuchsia}\left(5\right)}\end{array}\right] = \left[\begin{array}{ccc}3 & 1 & 4\\5 & 7 & 5\\1 & 3 & 5\end{array}\right]$$$
Answer
$$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 0 & 4\\0 & 1 & 0\end{array}\right] + \left[\begin{array}{ccc}2 & 1 & 4\\5 & 7 & 1\\1 & 2 & 5\end{array}\right] = \left[\begin{array}{ccc}3 & 1 & 4\\5 & 7 & 5\\1 & 3 & 5\end{array}\right]$$$A