Solving simultaneous equations with matrices Quiz

1. A system of three equations has a coefficient matrix with non-zero determinant. What is true?

• A. No solution; planes form a prism
• B. Exactly one solution; planes meet at a point
• C. Infinitely many solutions; planes meet in a line
• D. No solution; planes are parallel

2. The planes $x+y+z=1$, $x+y+z=2$ and $x+y+z=3$ are:

• A. meeting at a point
• B. a triangular prism
• C. meeting in a line
• D. three parallel planes

3. The planes $x+y+z=1$, $2x+2y+2z=2$ and $3x+3y+3z=3$ are:

• A. three coincident planes
• B. three parallel distinct planes
• C. a triangular prism
• D. meeting at a point

4. The planes $x+y=1$, $y+z=1$ and $x-z=1$ have a zero determinant. What is the arrangement?

• A. They meet at a point
• B. They meet in a line
• C. A triangular prism
• D. Two are parallel

5. $\mathbf{A}\mathbf{x}=\mathbf{b}$ has $\det\mathbf{A}=0$ and the equations are consistent. What is true?

• A. There is a unique solution
• B. There are infinitely many solutions
• C. $\mathbf{A}$ has an inverse
• D. There is no solution