Question

If , and , then compute and . Also, verify that

Answer 1

The given matrices are,

A=[ 1 2 −3 5 0 2 1 −1 1 ] B=[ 3 −1 2 4 2 5 2 0 3 ] C=[ 4 1 2 0 3 2 1 −2 3 ]

Find the value of ( A+B ).

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

Now, solve for ( B−C ).

B−C=[ 3 −1 2 4 2 5 2 0 3 ]−[ 4 1 2 0 3 2 1 −2 3 ] =[ 3−4 −1−1 2−2 4−0 2−3 5−2 2−1 0−( −2 ) 3−3 ] =[ −1 −2 0 4 −1 3 1 2 0 ]

This gives the value of ( A+B ) as [ 4 1 −1 9 2 7 3 −1 4 ] and ( B−C ) as [ −1 −2 0 4 −1 3 1 2 0 ].

Now, verify the equation.

A+( B−C )=( A+B )−C(1)

Substitute the value of ( B−C ) to the left side of equation (1).

A+( B−C )=[ 1 2 −3 5 0 2 1 −1 1 ]+[ −1 −2 0 4 −1 3 1 2 0 ] =[ 1+( −1 ) 2+( −2 ) −3+0 5+4 0+( −1 ) 2+3 1+1 −1+2 1+0 ] =[ 0 0 −3 9 −1 5 2 1 1 ]

Again, substitute the value of ( A+B ) to the right side of equation (1).

( A+B )−C=[ 4 1 −1 9 2 7 3 −1 4 ]−[ 4 1 2 0 3 2 1 −2 3 ] =[ 4−4 1−1 −1−2 9−0 2−3 7−2 3−1 −1−( −2 ) 4−3 ] =[ 0 0 −3 9 −1 5 2 1 1 ]

Hence, A+( B−C )=( A+B )−C is verified.