Question

How do you simplify `5[(0,-1,7,2)]+3[(5,-8,10,-4)]`?

Answer 1

`5[(0,-1,7,2)]+3[(5,-8,10,-4)]=[(15,-29,65,-2)]`

Explanation:

Here two operations are involved `-` One, multiplication of `1xx4` matrics by a scalar and Two - addition of thetwo outputs.

When we have a `mxxn` matrics by a scalar, each element of the matrics is multiplied by that scalar resulting in another `mxxn` matrics.

Further when two matrices `A` and `B`, both `mxxn` are added, each element of the first is added to respective elememt of second to get respeective element of resulting matrics.

For example if `a_(mn)` is the `n^(th)` element in `m^(th)` row of `A` matrics and `b_(mn)` is similar element of matrics `B`, we have `c_(mn)=a_(mn)+b_(mn)`, where `c_(mn)` is the respective element of the sum of the matrices.

Here we have two `1xx4` matrices `[(0,-1,7,2)]` and `[(5,-8,10,-4)]` and hence

`5[(0,-1,7,2)]+3[(5,-8,10,-4)]`

= `[(5xx0,5xx(-1),5xx7,5xx2)]+[(3xx5,3xx(-8),3xx10,3xx(-4))]`

= `[(0,-5,35,10)]+[(15,-24,30,-12)]`

= `[(0+15,-5+(-24),35+30,10+(-12))]`

= `[(15,-29,65,-2)]`