Simultaneous equations and planes Quiz

1. The equations $x+y+z=3$, $2x+2y+2z=6$ and $x-y=0$ have a determinant of

• A. $0$
• B. $1$
• C. $-2$
• D. $6$

2. A system has $\det\mathbf{M}=4$. The planes

• A. form a sheaf
• B. meet at one point
• C. form a prism
• D. are parallel

3. Which is the correct way to solve $\mathbf{M}\mathbf{x}=\mathbf{b}$?

• A. $\mathbf{x}=\mathbf{b}\mathbf{M}^{-1}$
• B. $\mathbf{x}=\mathbf{M}\mathbf{b}^{-1}$
• C. $\mathbf{x}=\mathbf{M}^{-1}\mathbf{b}$
• D. $\mathbf{x}=\mathbf{b}-\mathbf{M}$

4. The planes $x+y+z=1$, $x+y+z=2$ and $x-y=0$ form

• A. a sheaf
• B. a single point
• C. a line of intersection
• D. two parallel planes cut by a third

5. The equations $x+y+z=2$, $x-y+z=0$, $2x+2z=2$ have infinitely many solutions because

• A. the third equation is the sum of the first two on both sides
• B. the determinant is non-zero
• C. the planes are parallel
• D. the third equation has no $y$