Question 7:
(a) Find the inverse matrix of (3254).
(b) Ethan and Rahman went to the supermarket to buy cucumbers and carrots. Ethan bought 3 cucumbers and 2 carrots for RM9. Rahman bought 5 cucumbers and 4 carrots for RM16.
By using matrix method, find the price, in RM, of a cucumber and the price of a carrot.
Solution:
(a)Inverse matrix of (3254)=112−10(4−2−53)=12(4−2−53)=(2−1−5232)
(b)3x+2y=9.................(1)5x+4y=16...............(2)(3254)(xy)=(916) (xy)=(2−1−5232)(916) (xy)=((2)(9)+(−1)(16)(−52)(9)+(32)(16)) (xy)=(18−16−452+24) (xy)=(232)x=2, y=32∴
(a) Find the inverse matrix of (3254).
(b) Ethan and Rahman went to the supermarket to buy cucumbers and carrots. Ethan bought 3 cucumbers and 2 carrots for RM9. Rahman bought 5 cucumbers and 4 carrots for RM16.
By using matrix method, find the price, in RM, of a cucumber and the price of a carrot.
Solution:
(a)Inverse matrix of (3254)=112−10(4−2−53)=12(4−2−53)=(2−1−5232)
(b)3x+2y=9.................(1)5x+4y=16...............(2)(3254)(xy)=(916) (xy)=(2−1−5232)(916) (xy)=((2)(9)+(−1)(16)(−52)(9)+(32)(16)) (xy)=(18−16−452+24) (xy)=(232)x=2, y=32∴
Question 8:
The inverse matrix of
(a) Find the value of n and of t.
(b) Write the following simultaneous linear equations as matrix equation:
4x – y = 7
2x + 5y = –2
Hence, using matrix method, calculate the value of x and of y.
Solution:
The inverse matrix of
(a) Find the value of n and of t.
(b) Write the following simultaneous linear equations as matrix equation:
4x – y = 7
2x + 5y = –2
Hence, using matrix method, calculate the value of x and of y.
Solution: