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) 08(1) 1812(2) 8(24)5 ) =( 9 7 10 11 )