Question

For the matrices `A= [(2,1),(3,2)]` and B`[(-2,-2),(3,2)]`, how to calculate A+B, BA and kA?

Answer 1

See the explanation below

Explanation:

`A=((2,1),(3,2))`

`B=((-2,-2),(3,2))`

`"Matrix addition"`

`((a,b),(c,d))+((e,f),(g,h))=((a+e,b+f),(c+g,d+h))`

`A+B=((2,1),(3,2))+((-2,-2),(3,2))=((0,-1),(6,4))`

`"Matrix multiplication"`

`((a,b),(c,d))xx((e,f),(g,h))=((ae+bg,af+bh),(ce+gd,cf+dh))`

`BxxA=((-2,-2),(3,2))*((-2,-2),(3,2))=((-2,0),(0,-2))=-2I`

`I=((1,0),(0,1))`

`"Multiplication by a constant"`

`k xx((a,b),(c,d))=((ka,kb),(kc,k))`

`kA=k((2,1),(3,2))=((2k,k),(3k,2k))`