Matrices Long Questions (Question 4)


Question 4:
It is given that   Q( 3 2 5 4 )=( 1 0 0 1 ) , 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
Hence, using matrix method, calculate the value of x and y.

Solution:
(a)
Q= 1 3( 4 )( 5 )( 2 ) ( 4 2 5 3 ) = 1 2 ( 4 2 5 3 ) =( 2 1 5 2 3 2 )
(b)
( 3 2 5 4 )( x y )=( 7 9 )               ( x y )= 1 2 ( 4 2 5 3 )( 7 9 )               ( x y )= 1 2 ( ( 4 )( 7 )+( 2 )( 9 ) ( 5 )( 7 )+( 3 )( 9 ) )               ( x y )= 1 2 ( 10 8 )               ( x y )=( 5 4 ) x=5,  y=4