Question 3:
Solution:
(a)
Q=(3265)−1Q=13(5)−2(6)(5−2−63)Q=13(5−2−63)Q=(53−23−21)
(b)
(3265)(uv)=(52)(uv)=13(5−2−63)(52)(uv)=13((5)(5)+(−2)(2)(−6)(5)+(3)(2))(uv)=13(21−24)(uv)=(7−8)∴u=7,v=−8
It is given that Q
(3265)=(1001)
, where Q is a 2 x 2 matrix.
(a) Find Q.(b) Write the following simultaneous linear equations as matrix equation:
3u + 2v = 5
6u + 5v = 2
Hence, using matrix method, calculate the value of u and v.
Solution:
(a)
Q=(3265)−1Q=13(5)−2(6)(5−2−63)Q=13(5−2−63)Q=(53−23−21)
(b)
(3265)(uv)=(52)(uv)=13(5−2−63)(52)(uv)=13((5)(5)+(−2)(2)(−6)(5)+(3)(2))(uv)=13(21−24)(uv)=(7−8)∴u=7,v=−8
Question 4:
Hence, using matrix method, calculate the value of x and y.
Solution:
(a)
Q=13(−4)−(5)(−2)(−42−53)=−12(−42−53)=(2−152−32)
(b)
(3−25−4)(xy)=(79)(xy)=−12(−42−53)(79)(xy)=−12((−4)(7)+(2)(9)(−5)(7)+(3)(9))(xy)=−12(−10−8)(xy)=(54)∴x=5,y=4
It is given that
Q(3−25−4)=(1001)
, where Q is a 2 × 2 matrix.
(a) Find the matrix Q.
(b) Write the following simultaneous linear equations as matrix equation:
3x – 2y = 7
5x – 4y = 9
Solution:
(a)
Q=13(−4)−(5)(−2)(−42−53)=−12(−42−53)=(2−152−32)
(b)
(3−25−4)(xy)=(79)(xy)=−12(−42−53)(79)(xy)=−12((−4)(7)+(2)(9)(−5)(7)+(3)(9))(xy)=−12(−10−8)(xy)=(54)∴x=5,y=4