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 + 3= 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

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