Question

If and , then verify that (i) (ii)

Answer 1

(i)

The given matrices are,

A=[ −1 2 3 5 7 9 −2 1 1 ]

And,

B=[ −4 1 −5 1 2 0 1 3 1 ]

Calculate A+B,

A+B=[ −1 2 3 5 7 9 −2 1 1 ]+[ −4 1 −5 1 2 0 1 3 1 ] =[ −5 3 −2 6 9 9 −1 4 2 ]

The transpose of A+B is,

( A+B ) ′ =[ −5 6 −1 3 9 4 −2 9 2 ]

Calculate A ′ and B ′ and add.

A ′ + B ′ =[ −1 5 −2 2 7 1 3 9 1 ]+[ −4 1 1 1 2 3 −5 0 1 ] =[ −5 6 −1 3 9 4 −2 9 2 ]

Therefore, it is verified that ( A+B ) ′ = A ′ + B ′ .

(ii)

The given matrices are,

A=[ −1 2 3 5 7 9 −2 1 1 ]

And,

B=[ −4 1 −5 1 2 0 1 3 1 ]

Calculate A−B,

A−B=[ −1 2 3 5 7 9 −2 1 1 ]−[ −4 1 −5 1 2 0 1 3 1 ] =[ 3 1 8 4 5 9 −3 −2 0 ]

The transpose of A−B is,

( A−B ) ′ =[ 3 4 −3 1 5 −2 8 9 0 ]

Calculate A ′ and B ′ and subtract.

A ′ − B ′ =[ −1 5 −2 2 7 1 3 9 1 ]−[ −4 1 1 1 2 3 −5 0 1 ] =[ 3 4 −3 1 5 −2 8 9 0 ]

Therefore, it is verified that ( A−B ) ′ = A ′ − B ′ .