Reduced Row Echelon Form (RREF) Caclulator

The calculator will find the row echelon form (simple or reduced - RREF) of the given (augmented) matrix (with variables if needed), with steps shown.

Show Instructions
  • In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`.
  • In general, you can skip parentheses, but be very careful: e^3x is `e^3x`, and e^(3x) is `e^(3x)`.
  • Also, be careful when you write fractions: 1/x^2 ln(x) is `1/x^2 ln(x)`, and 1/(x^2 ln(x)) is `1/(x^2 ln(x))`.
  • If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx.
  • Sometimes I see expressions like tan^2xsec^3x: this will be parsed as `tan^(2*3)(x sec(x))`. To get `tan^2(x)sec^3(x)`, use parentheses: tan^2(x)sec^3(x).
  • Similarly, tanxsec^3x will be parsed as `tan(xsec^3(x))`. To get `tan(x)sec^3(x)`, use parentheses: tan(x)sec^3(x).
  • From the table below, you can notice that sech is not supported, but you can still enter it using the identity `sech(x)=1/cosh(x)`.
  • If you get an error, double check your expression, add parentheses and multiplication signs where needed, and consult the table below.
  • All suggestions and improvements are welcome. Please leave them in comments.
The following table contains the supported operations and functions:
TypeGet
Constants
ee
pi`pi`
ii (imaginary unit)
Operations
a+ba+b
a-ba-b
a*b`a*b`
a^b, a**b`a^b`
sqrt(x), x^(1/2)`sqrt(x)`
cbrt(x), x^(1/3)`root(3)(x)`
root(x,n), x^(1/n)`root(n)(x)`
x^(a/b)`x^(a/b)`
abs(x)`|x|`
Functions
e^x`e^x`
ln(x), log(x)ln(x)
ln(x)/ln(a)`log_a(x)`
Trigonometric Functions
sin(x)sin(x)
cos(x)cos(x)
tan(x)tan(x), tg(x)
cot(x)cot(x), ctg(x)
sec(x)sec(x)
csc(x)csc(x), cosec(x)
Inverse Trigonometric Functions
asin(x), arcsin(x), sin^-1(x)asin(x)
acos(x), arccos(x), cos^-1(x)acos(x)
atan(x), arctan(x), tan^-1(x)atan(x)
acot(x), arccot(x), cot^-1(x)acot(x)
asec(x), arcsec(x), sec^-1(x)asec(x)
acsc(x), arccsc(x), csc^-1(x)acsc(x)
Hyperbolic Functions
sinh(x)sinh(x)
cosh(x)cosh(x)
tanh(x)tanh(x)
coth(x)coth(x)
1/cosh(x)sech(x)
1/sinh(x)csch(x)
Inverse Hyperbolic Functions
asinh(x), arcsinh(x), sinh^-1(x)asinh(x)
acosh(x), arccosh(x), cosh^-1(x)acosh(x)
atanh(x), arctanh(x), tanh^-1(x)atanh(x)
acoth(x), arccoth(x), cot^-1(x)acoth(x)
acosh(1/x)asech(x)
asinh(1/x)acsch(x)

Choose the dimension of the matrix: z$$$\times$$$

Enter the elements of the matrix

Write all suggestions in comments below.

Solution

Your input: find the reduced row echelon form of $$$A=\left[ \begin{array}{ccc} 1 & 5 & 1 \\\\ 2 & 11 & 5 \end{array} \right]$$$

Make zeros in column 1 except entry at row 1, column 1 (pivot entry).

Subtract row 1 multiplied by $$$2$$$ from row 2 $$$\left(R_2=R_2-\left(2\right)R_1\right)$$$:

$$$\left[ \begin{array}{ccc} 1 & 5 & 1 \\\\ 0 & 1 & 3 \end{array} \right]$$$

Make zeros in column 2 except entry at row 2, column 2 (pivot entry).

Subtract row 2 multiplied by $$$5$$$ from row 1 $$$\left(R_1=R_1-\left(5\right)R_2\right)$$$:

$$$\left[ \begin{array}{ccc} 1 & 0 & -14 \\\\ 0 & 1 & 3 \end{array} \right]$$$

Answer: $$$\text{rref}(A)=\left[ \begin{array}{ccc} 1 & 0 & -14 \\\\ 0 & 1 & 3 \end{array} \right]$$$