a) Find a weak formulation for the partial differential equation{\partial u\over\partial t

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

Differentiate the Gaussian elimination and LU- Factorization in solving system of linear equations.

Do the equations 5y−2x=18
and
6x=−4y−10
form a system of linear equations? Explain.

Find values of a and b such that the system of linear equations has (a) no solution, (b) exactly one solution, and (c) infinitely many solutions.
x + 2y = 3
ax + by = −9

Do the equations 4x−3y=54x−3y=5 and 7y+2x=−87y+2x=−8 form a system of linear equations? Explain

Task:
For ${\displaystyle n\in \mathbb{N}}$ and ${\displaystyle W\le {\mathbb{F}}^n}$, show that there exists a homogeneous system of linear equations whose solution space is W.
My work:
Since ${\displaystyle W\le {\mathbb{F}}^n,k=\dim \left(W\right)\le \dim \left({\mathbb{F}}^n\right)}$. Let's say that ${\displaystyle \{w_1,w_2,\dots ,w_k\}}$ is a basis of W. Now, construct a matrix A (of size ${\displaystyle k\times n}$) such that its rows are elements from the basis of W, stacked together. The row space of A is W, so the row space of its row-echelon form is W too. At this point, I'm stuck! I'm trying to come up with a homogeneous system with the help of A, though there may exist other easier ways of approaching this problem.
Could someone show me the light?
P.S. ${\displaystyle W\le {\mathbb{F}}^n}$ stands for W is a subspace of ${\displaystyle {\mathbb{F}}^n}$.
P.P.S. Isn't this equivalent to saying that W is the null-space of some matrix? Can we go ahead along these lines, and construct a matrix P such that ${\displaystyle Pw=0}$ for all ${\displaystyle w\in W}$?

Write the correct equation for this line.
${\displaystyle y–y_1=m\left(x–x_1\right)}$, when the slope is 4 and a line passes through the point (-3. 3).