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4.10 SPM Practice (Long Questions)

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Question 5:
(a) Given 114(2s−4t)(t−142)=(1001), find the value of s and of t.
(b) Write the following simultaneous linear equations as matrix form:
3x – 2y = 5
9x + y = 1
Hence, using matrix method, calculate the value of x and y.

Solution:
(a)114(2s−4t)(t−142)=(1001)114(2t+4s−2+2s−4t+4t4+2t)=(1001)−2+2s14=0 2s=2    s=14+2t14=14+2t=142t=10t=5

(b)(3−291)(xy)=(51)  (xy)=121(12−93)(51)  (xy)=121((1)(5)+(2)(1)(−9)(5)+(3)(1))  (xy)=121(7−42)  (xy)=(13−2)∴



Question 6:
It is given that matrix P=( 6 −3 −5 2 ) and matrix Q= 1 m ( 2 3 5 n )  such that PQ=( 1 0 0 1 ).
(a) Find the value of m and of n.
(b) Write the following simultaneous linear equations as matrix form:
6x – 3y = –24
–5x + 2y = 18
Hence, using matrix method, calculate the value of x and y.

Solution:
(a) m=6( 2 )−( −3 )( −5 )   =12−15 m=−3 n=6

(b) ( 6 −3 −5 2 )( x y )=( −24 18 )   ( x y )= 1 12−15 ( 2 3 5 6 )( −24 18 )   ( x y )= 1 −3 ( ( 2 )( −24 )+( 3 )( 18 ) ( 5 )( −24 )+( 6 )( 18 ) )   ( x y )= 1 −3 ( 6 −12 )   ( x y )=( −2 4 ) ∴x=−2,  y=4