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4.9 SPM Practice (Short Questions)

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4.9.2 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)
3x – x = 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 ) ) = ( 15 − 8 − 10 − 6 ) = ( 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 ) ) = ( 2 − 12 − 3 + 0 4 − 3 ) = ( − 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)