(Solved): Could you please help me to solve these equations with the steps? Thanks! Problem \#6: Consider t ...

Could you please help me to solve these equations with the steps? Thanks!

Problem \#6: Consider the system of linear equations $$\begin{array}{r}?7x_1?8x_2?8x_3+x_4=0\\ 14x_1+5x_2+8x_3+11x_4=0\\ ?105x_1?43x_2?64x_3?76x_4=0\\ 7x_1?14x_2?8x_3+25x_4=0\end{array}$$ True or False: the system has a unique solution. Problem \#6: Problem \#7: Consider the following matrices $$\begin{array}{l}\mathbf{x}=\left[\begin{array}{c}4\\ 3\\ \frac{14}{3}\end{array}\right],A=\left[\begin{array}{cccc}2& 5& 3& 2\\ 0& ?1& 3& 4\\ ?1& ?2& ?1& ?2\end{array}\right],B=\left[\begin{array}{ccc}\frac{1}{2}& \frac{2}{3}& ?\frac{6}{7}\\ \frac{3}{4}& ?\frac{1}{3}& ?\frac{3}{7}\\ \frac{1}{4}& ?\frac{1}{3}& 0\end{array}\right],C=\\ \left[\begin{array}{ccc}4& ?4& 0\\ ?6& 14& 4\\ 0& ?\frac{14}{3}& 3\end{array}\right]\end{array}$$ Which of the matrices $$A,B,C$$ is such that $$M\mathrm{x}=0$$ ? Problem \#8: Determine the value of $$b$$ that would guarantee that the below linear system is consistent. $$\begin{array}{r}{x}_1?2x_2?6x_3=?6\\ 2x_1?4x_2?6x_3=2\\ ?2x_1+4x_2?6x_3=b\end{array}$$ Problem \# 8: Problem \#9: Consider the matrices $$\begin{array}{c}\mathbf{b}=\left[\begin{array}{c}?5\\ ?4\\ 2\end{array}\right],A=\left[\begin{array}{ccc}?\frac{5}{2}& ?\frac{5}{3}& 0\\ ?\frac{4}{3}& ?\frac{4}{3}& ?\frac{4}{3}\\ \frac{2}{7}& \frac{2}{7}& \frac{2}{7}\end{array}\right],B=\left[\begin{array}{ccc}?\frac{5}{2}& ?\frac{5}{3}& 0\\ ?\frac{4}{3}& 0& ?\frac{4}{3}\\ \frac{2}{7}& \frac{2}{7}& \frac{2}{7}\end{array}\right],C=\\ \left[\begin{array}{ccc}?\frac{5}{2}& ?\frac{4}{3}& \frac{2}{7}\\ ?\frac{5}{3}& 0& \frac{2}{7}\\ 0& ?\frac{4}{7}& \frac{2}{7}\end{array}\right]\end{array}$$ For which matrices is the matrix equation $$M\mathbf{x}=\mathbf{b}$$ consistent? (A) $$C$$ only (B) $$B$$ and $$C$$ only (C) $$B$$ only (D) $$A$$ and $$B$$ only (E) none of them (F) all of them (G) $$A$$ and $$C$$ only (H) $$A$$ only