O-LevelAdditional MathematicsSimultaneous equations4037/12 · May/June 2014 · Q67 Marks
Matrices X, Y and Z are such that X = beginpmatrix 2 & 3 1 & 1/2 endpmatrix, Y = beginpmatrix 1 & 3 4 & 5 6 & 7 endpmatrix and Z = beginpmatrix 1 & 2 & 3 endpmatrix. Write down all the matrix products which are possible using any two of these matrices. Do not evaluate these products.
- (a)Matrices X, Y and Z are such that X = beginpmatrix 2 & 3 1 & 1/2 endpmatrix, Y = beginpmatrix 1 & 3 4 & 5 6 & 7 endpmatrix and Z = beginpmatrix 1 & 2 & 3 endpmatrix. Write down all the matrix products which are possible using any two of these matrices. Do not evaluate these products.[2]
- (b)Matrices A and B are such that A = \begin{pmatrix} 5 & -2 \\ -4 & 1 \end{pmatrix} and AB = \begin{pmatrix} 3 & 9 \\ -6 & -3 \end{pmatrix}. Find the matrix B.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B1,B1] (a) B1 for each, must be in correct order,
- [M1] (b) M1 for pre-multiplication by A⁻¹
- [B1,B1] (b) B1 for - 1/3 B1 for beginpmatrix 1 & 2 4 & 5 endpmatrix
- [DM1] (b) DM1 for attempt at matrix multiplication
- [A1] (b) A1 allow in either form
- [M1] (b) M1 for a complete method to obtain 4 equations
- [A2,1,0] (b) -1 for each incorrect equation
- [M1] (b) M1 for solution to find 4 unknowns
- [A1] (b) A1 for a correct, final matrix
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →