Multiplication of a Matrix by a Number (Sample Questions)


Example 1:
Express the following as single matrix.

(a) 3 ( 1 4 3 2 ) + 2 ( 3 1 3 4 )

(b) 2 ( 1 0 9 4 ) 4 ( 2 2 3 6 ) 1 3 ( 9 3 6 15 )

Solution:
(a) 3 ( 1 4 3 2 ) + 2 ( 3 1 3 4 ) = ( 3 × 1 3 × ( 4 ) 3 × ( 3 ) 3 × 2 ) + ( 2 × ( 3 ) 2 × 1 2 × 3 2 × ( 4 ) ) = ( 3 12 9 6 ) + ( 6 2 6 8 ) = ( 3 + ( 6 ) 12 + 2 9 + 6 6 ( 8 ) ) = ( 3 10 3 14 )


(b) 2 ( 1 0 9 4 ) 4 ( 2 2 3 6 ) 1 3 ( 9 3 6 15 ) = ( 2 0 18 8 ) ( 8 8 12 24 ) ( 1 3 × ( 9 ) 1 3 × ( 3 ) 1 3 × ( 6 ) 1 3 × 15 ) = ( 2 0 18 8 ) ( 8 8 12 24 ) ( 3 1 2 5 ) = ( 2 ( 8 ) ( 3 ) 0 8 ( 1 ) 18 12 ( 2 ) 8 ( 24 ) 5 ) = ( 9 7 10 11 )


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