Solving simultaneous equations with matricesAQA A-Level Further Maths: Mind map

Exam questions on Solving simultaneous equations with matrices

1. Three planes have equations $x+y+z=6$, $2x-y+z=6$ and $x+3y-z=2$. A calculator may be used.
   The inverse of the coefficient matrix is $\frac18\begin{pmatrix}-2&4&2\\3&-2&1\\7&-2&-3\end{pmatrix}$. Use it to solve the equations.2 marks
2. Three planes have equations $x+y-z=2$, $2x+2y-2z=4$ and $x-y+z=0$.
   Find the general solution of the three equations.2 marks
3. Three planes have equations $x+2y+z=4$, $2x+y-z=1$ and $3x+3y=k$, where $k$ is a constant.
   Show that the three equations have no solution when $k=7$, and state the geometrical arrangement of the planes.3 marks