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

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