# Answer to Question #21506 in Algebra for lishan hailu

Question #21506

A=(0 2 3) (7 6 3)

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

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

Expert's answer

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)

(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)

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