Question

Show that (i) (ii)

Answer 1

(i)

Simplifying the left hand side of given matrix equation,

[ 5 −1 6 7 ][ 2 1 3 4 ]=[ 5×2−1×3 5×1−1×4 6×2+7×3 6×1+7×4 ] =[ 7 1 33 34 ]

Now simplifying right hand side of the given matrix equation,

[ 2 1 3 4 ][ 5 −1 6 7 ]=[ 2×5+1×6 2( −1 )+1×7 3×5+4×6 3( −1 )+4×7 ] =[ 16 5 39 25 ]

Since left hand side is not equal to right hand side.

Hence, it is proved that [ 5 −1 6 7 ][ 2 1 3 4 ]≠[ 2 1 3 4 ][ 5 −1 6 7 ].

(ii)

Simplifying the right hand side of given matrix equation,

[ 1 2 3 0 1 0 1 1 0 ][ −1 1 0 0 −1 1 2 3 4 ]=[ −1+0+6 1−2+9 0+2+12 0+0+0 0−1+0 0+1+0 −1+0+0 1−1+0 0+1+0 ] =[ 5 8 14 0 −1 1 −1 0 1 ]

Simplifying left hand side of given matrix equation,

[ −1 1 0 0 −1 1 2 3 4 ][ 1 2 3 0 1 0 1 1 0 ]=[ −1+0+0 −2+1+0 −3+0+0 0+0+1 0−1+1 0+0+0 2+0+4 4+3+4 6+0+0 ] =[ −1 −1 −3 1 0 0 6 11 6 ]

Since left hand side is not equal to right hand side.

Hence, it is proved that [ −1 1 0 0 −1 1 2 3 4 ][ 1 2 3 0 1 0 1 1 0 ]≠[ 1 2 3 0 1 0 1 1 0 ][ −1 1 0 0 −1 1 2 3 4 ].