2.10.4 Matrices, SPM Paper 2 (Long Question)


Question 10:
It is given that matrix M is a 2 × 2 matrix such that
M( −2   1 1      3 )=( 1    0 0    1 )
(a) Find matrix M.
(b)   Write the following simultaneous linear equations as matrix equations:
–2x + y = 10
x + 3y = 9      
Hence, using matrix method, calculate the value of x and of y. [6 marks]
 
Solution:
(a)
R= ( −2   1 1      3 ) −1   = 1 ( −2 )( 3 )−( 1 )( 1 ) ( 3     −1 −1   −2 )   =− 1 7 ( 3     −1 −1   −2 )   =( − 3 7       1 7 1 7          2 7 )

(b)
( −2   1 1      3 )( x y )=( 10 9 ) ( x y )= 1 ( −2 )( 3 )−( 1 )( 1 ) ( 3     −1 −1   −2 )( 10 9 ) ( x y )=− 1 7 ( 3×10+( −1 )( 9 ) −1×10+( −2 )( 9 ) ) ( x y )=− 1 7 ( 21 −28 ) ( x y )=( −3 4 ) x=−3, y=4

Leave a Comment