Answer to Question #21506 in Algebra for lishan hailu

Question

A=(0 2 3) (7 6 3)
(2 1 4) and B= (1 4 5)then the value of c=2A+3B is.......

Answer 1

The matrix 2A is obtained from A by multiplying eachcoefficient of A by 2, so 2A =
(2*0 2*2 2*3)
(2*2 2*1 2*4)
=
(0 4 6)
(4 2 8)
Similarly, 3B =(3*1 3*4 3*5)
(3*7 3*6 3*3)
=
(3 12 15)
(21 18 9)
The sum of matrices 2A+3B is the matrix whose coeficientsare sums of the corresponding coefficients of 2A and 3B: C = 2A + 3B =(0 4 6)
(4 2 8)
+
(3 12 15)
(21 18 9)
=
(0+3 4+12 6+15)
(4+21 2+18 8+9)
=
(3 16 21)
(25 20 17)