Question

2 41I. Let A=,C=Find each of the following:(i) A B(iv) AB(i) 3A - C(v) BA

Answer 1

Consider the given matrices as shown below,

A=[ 2 4 3 2 ] . B=[ 1 3 −2 5 ] and C=[ −2 5 3 4 ]

(i)

A+B=[ 2 4 3 2 ]+[ 1 3 −2 5 ] =[ 2+1 4+3 3−2 2+5 ] =[ 3 7 1 7 ]

(ii)

A−B=[ 2 4 3 2 ]−[ 1 3 −2 5 ] =[ 2−1 4−3 3+2 2−5 ] =[ 1 1 5 −3 ]

(iii)

3A−C=3[ 2 4 3 2 ]−[ −2 5 3 4 ] =[ 3×2 3×4 3×3 3×2 ]−[ −2 5 3 4 ] =[ 6 12 9 6 ]−[ −2 5 3 4 ] =[ 8 7 6 2 ]

(iv)

AB=[ 2 4 3 2 ][ 1 3 −2 5 ] =[ 2( 1 )+4( −2 ) 2( 3 )+4( 5 ) 3( 1 )+2( −2 ) 3( 3 )+2( 5 ) ] =[ 2−8 6+20 3−4 9+10 ] =[ −6 26 −1 19 ]

(v)

BA=[ 1 3 −2 5 ][ 2 4 3 2 ] =[ 1( 2 )+3( 3 ) 1( 4 )+3( 2 ) −2( 2 )+5( 3 ) −2( 4 )+5( 2 ) ] =[ 2+9 4+6 −4+15 −8+10 ] =[ 11 10 11 2 ]