Matrices

A^t - transpose – switch rows and columns

To add matrices they must be the same dimensions(row x column)

To add matrices you add corresponding entries

To complete scalar multiplication you multiply every entry by the number

Ex 1. A = [ 3 8 1 ] B = [ 2 0 9 ]

[ 4 0 -3 ] [ 4 -6 -5 ]

[ -2 1 5 ] [ 0 7 2 ]

a. What are the dimensions of A and B? A = 3x3 B = 3x3

b. Find A^t and B^t A^t = [ 3 4 -2 ] B^t = [ 2 4 0 ]

[ 8 0 1 ] [ 0 -6 7 ]

[ 1 -3 5 ] [ 9 -5 2 ]

c. Find A + B A + B = [ 5 8 10 ]

[ 8 -6 -8 ]

[ -2 8 7 ]

d. Find 4A – 2B 4A = [ 12 32 4 ] 2B = [ 4 0 18 ] 4A – 2B = [ 8 32 -14 ]

[ 16 24 -12 ] [ 8 -12 -10 ] [ 8 12 -2 ]

[ -8 4 20 ] [ 0 14 4 ] [ -8 -10 16 ]