Matrices

(a bc d )±(e f

g h)=(a±e b± fc± g d±h)

(a bc d )( pq )=(ap+bqcp+dq )

(a bc d )( p q

r s )=(ap+br aq+bscp+dr cq+ds)

3

2A – 5B¿2(82)−5( 1−4) ¿(164 )−( 5−20) ¿(1124)

Example

The 2x2 identity matrix is called I, where:

I¿(1 00 1)

When a matrix is multiplied by the identity matrix I, it stays the same.

Find 2A – 5B, where A¿(82) and B¿( 1−4).

AB¿(3 42 5)(2 −1

6 7 ) ¿(3×2+4×6 3×−1+4×7

2×2+5×6 2×−1+5×7 ) ¿(30 25

34 33)BA¿(2 −1

6 7 )(3 42 5 )

Find AB and BA where A¿(3 42 5) and B¿(2 −1

6 7 )

Example