4.9 Matrices, SPM Practice (Short Questions)


4.9 Matrices, SPM Practice (Short Questions)
Question 5:
Given that ( 3   x )( x 1 )=( 18 ),  find the value of x.

Solution:
( 3   x )( x 1 )=( 18 )
[3 × x + x (–1)] = (18)
3xx = 18
2x = 18
x = 9


Question 6:
( 3 4 2 3 )( 5 2 )=  


Solution:
( 3 4 2 3 )( 5 2 )=( ( 3 )( 5 )+( 4 )( 2 ) ( 2 )( 5 )+( 3 )( 2 ) )                       =( 158 106 )                       =( 7 16 )



Question 7:
( 2 4 3 4 0 1 )( 1 3 )=

Solution:
Order of the product of the two matrices
=( 3 ×2 )( 2× 1 )=( 3×1 )

( 2 4 3 4 0 1 )( 1 3 )=( 2( 1 )+4( 3 ) ( 3 )( 1 )+0( 3 ) ( 4 )( 1 )+1( 3 ) )                      =( 212 3+0 43 )                      =( 10 3 1 )



Question 8:
( 1  1   2 )( 5 1 3 2 0 4 )=

Solution:
Order of the product of the two matrices
=( 1 ×3 )( 3× 2 )=( 1×2 )

( 1  1   2 )( 5 1 3 2 0 4 )=
= (1×5 + (–1)(–3) + (2)(2)  1×1 + (–1)(0) + (2)(4))
= (5 + 3 + 4   1 + 0 + 8)
= (12   9)