please include details Thank you Given A 6 3 6 B 2 4 2 u a 3

please include details. Thank you

Given A -6 3 6 B 2 4 -2, u a -3 v- 2 Caleulate liv a dot prodrarte of rows of B und v

Solution

a) A = [1 2 4; -5 3 6 ; 2 3 1]

u = [7;-3;2]

Au = [9;-32;7];

we have to calculate Au in linear combination of columns of A ie

(1 -5 2) ; (2,3,3);(4 6 1)

let respective coefficient be a,b,c

so  [9;-32;7] = a(1 -5 2)+b (2,3,3)+ c(4 6 1)

9 = a+2b+4c

-32 = -5a+3b+6c

7 = 2a+3b+c

solving we get ,

a = 7;b=-3; c = 2

[9;-32;7] = 7* (1 -5 2) -3 * (2,3,3)+2* (4 6 1)

b) B = [3 -3 6; 2 4 -2 ; 4 2 -3];

v = [9 ;2 ;-3];

we have to calculate Bv as dot product of rows of B and v

B1 = 1st row of B = (3 -3 6);

B2= 2nd row = (2 4 -2);

B3 = 3rd row =(4 2 -3);

Bv = [3;32;85];

where v = [9 2 3];

Bv = [B1. v ; B2.v ; B3.v]