RREF of $$$\left[\begin{array}{c}\sin{\left(x \right)}\\\cos{\left(x \right)}\end{array}\right]$$$

The calculator will find the reduced row echelon form of the $$$2$$$x$$$1$$$ matrix $$$\left[\begin{array}{c}\sin{\left(x \right)}\\\cos{\left(x \right)}\end{array}\right]$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

Reduced?

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Your Input

Find the reduced row echelon form of $$$\left[\begin{array}{c}\sin{\left(x \right)}\\\cos{\left(x \right)}\end{array}\right]$$$.

Solution

Divide row $$$1$$$ by $$$\sin{\left(x \right)}$$$: $$$R_{1} = \frac{R_{1}}{\sin{\left(x \right)}}$$$.

$$$\left[\begin{array}{c}1\\\cos{\left(x \right)}\end{array}\right]$$$

Subtract row $$$1$$$ multiplied by $$$\cos{\left(x \right)}$$$ from row $$$2$$$: $$$R_{2} = R_{2} - \cos{\left(x \right)} R_{1}$$$.

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

Answer

The reduced row echelon form is $$$\left[\begin{array}{c}1\\0\end{array}\right]$$$A.