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

1 Answer
Jan 20, 2018

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))