AQA A Level Further Maths
Topic questions Pure mathematics Simultaneous equations
6 questions · 60 marks · about 1 hour
The matrix M is defined as
where k is a constant.
State any restrictions on the value of k
The matrix M is defined as
where c is a real number.
The linear transformation T is represented by the matrix M
Show that, for one particular value of c, the image under T of every point lies in the plane
State the value of c for which this occurs.
It is given that M is a non-singular matrix.
State any restrictions on the value of c
Using your answer from part (b)(ii), solve
The matrix M is defined as
where k is a constant.
State any restrictions on the value of k
Using your answer to part (a)(i), solve
State any restrictions on the value of p.
The equations below represent three planes.
Find, in terms of p, the coordinates of the point of intersection of the three planes.
In the case where p 
2, show that the planes are mutually perpendicular.
Three planes have equations
The planes do not meet at a unique point.
Show that k 4
5 is one possible value of k, and find the other possible value of k.
For each value of k found in part (a), identify the configuration of the given planes.
In each case fully justify your answer, stating whether or not the equations of the planes form a consistent system.
Three planes have equations
where k is a real constant.
The planes do not meet at a unique point.
Find the possible values of k.
For each value of k found in part (a), identify the configuration of the given planes.
Fully justify your answer, stating in each case whether or not the equations of the planes form a consistent system.
Memes
Laugh now. Cry in the exam hall later. Then come back and do a past paper.
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