Determine whether the statement is true or false. If the last row of the reduced row echelon form of an augmented matrix of a system of linear equatio

Determine whether the given set S is a subspace of the vector space V.
A. V=$P_5$, and S is the subset of $P_5$ consisting of those polynomials satisfying p(1)>p(0).
B. $V=R_3$, and S is the set of vectors $(x_1,x_2,x_3)$ in V satisfying $x_1-6x_2+x_3=5$.
C. $V=R^n$, and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
D. V=$C^2(I)$, and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.
E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.
F. V=$P_n$, and S is the subset of $P_n$ consisting of those polynomials satisfying p(0)=0.
G. $V=M_n(R)$, and S is the subset of all symmetric matrices

Can someone show me step-by-step how to diagonalize this matrix? Im

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations $\{\begin{array}{l}9x-3y+z=13\\ 12x-8z=5\\ 3x+4y-z=6\end{array}$

Reduce the system of linear equations to upper triangular form and solve.
$\{\begin{array}{l}3x-y=1\\ -3x+y=4\end{array}$

The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.
$\lambda 1=2\Rightarrow \{[4,3,1]\},\lambda 2=-2\Rightarrow \{[1,2,0],[2,3,1]\}$

Write the system of linear equations in the form ${\displaystyle Ax=b}$ and solve this matrix equation for x. ${\displaystyle -x_1+x_2=4}$
${\displaystyle -2x_1+x_2=0}$

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1,x2,x3,x4x as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. ⎡⎣⎢100010000002⎤⎦⎥