The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix.

Find the linear approximation of the function $f(x)=\sqrt{4-x}$ at $a=0$
Use L(x) to approximate the numbers $\sqrt{3.9}$ and $\sqrt{3.99}$ Round to four decimal places

Find the augmented matrix for the following system of linear equations:
$\{\begin{array}{l}5x+7y-36z=38\\ -8x-11y+57z=-60\end{array}$

Please, write the given expression in standard form of linear equations by solving for x.
x – 8 = 0

Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. All vectors (x, y, z) in $V_3$ whose components satisfy a system of three linear equations of the form:
$a_{11}x+a_{12}y+a_{13}z=0$
$a_{21}x+a_{22}y+a_{23}z=0$
$a_{31}x+a_{32}y+a_{33}z=0$

If I get the slope of a line, and one point that is on it, then, are they define exactly ONE line?
The point–slope form of linear equations ${\displaystyle (y-y_1=m(x-x_1))}$ need only the slope and the coordinates of that given point. And this equation describes exactly one line.
Is it enough?

How would you solve the following system of linear equations:
${\displaystyle 2x_1+(3+a)x_2+2x_3=2+a}$
${\displaystyle x_1+a{x}_2+2x_3=a}$
${\displaystyle a{x}_1+2x_2+2a{x}_3=0}$
assuming that ${\displaystyle a\ne \pm \sqrt{2}}$? I feel confident in solving linear equation systems with just constants as the coefficients but the variable coefficient a is what gives me problems.
Here is the solution I find: solution as augmented matrix but how would the assumption about a make the reduced echelon form any different compared to an assumption about e.g.${\displaystyle a\ne \pm \sqrt{2}}$?

Answer true or false to each of the following statements and explain your answers.
a. Polynomial regression equations are useful for modeling more complex curvature in regression equations than can be handled by using the method of transformations.
b. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.
c. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.