# What is the product of the following matrices?  4   5   6 1   3   5 and 1 4 3 6 2 6

hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the matrices:

A =  4  5  6                  B =  1    4

1  3  5                          3    6

2     6

We need to find the product of AxB

We notice that A is ( 2x3 ) and B is ( 3x2)

Then the product will be a (2x2) matrix.

==>AxB

AB11 =  4*1 + 5*3 + 6*2 = 4+ 15 + 12 = 31

AB12 = 4*4 + 5*6  + 6*6 = 16 + 30 + 36 =  82

AB 21 = 1*1 + 3*3 + 5*2 = 1 + 9 + 10 = 20

AB22 = 1 * 4 + 3*6 + 5*6 = 4 + 18 + 30 = 52

Then the matrix AxB is :

AxB =     31     82

=>          20     52

justaguide | College Teacher | (Level 2) Distinguished Educator

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When we multiply a 2X3 matrix with a 3X2 matrix we get a 2X2 matrix. Now the term T11 of the resulting matrix is equal to the sum of the products of each term in the first row of first matrix with the corresponding terms in the first column of the 2nd matrix.

We have matrices given as

4   5   6

1   3   5

and

1   4

3   6

2   6

So T11 = 4*1 + 5*3 + 6*2 = 4 + 15 + 12 = 31.

Similarly T12 = 4*4 + 5*6 + 6*6 = 16 + 30 + 36 = 82

T21 = 1*1 + 3*3 + 5*2 = 1 + 9 + 10 = 20

T22 = 1*4 + 3*6 + 5*6 = 4 + 18 + 30 = 52

The matrix resulting from the multiplication is:

31   82

20   52

neela | High School Teacher | (Level 3) Valedictorian

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The product of the two matrices A = [(4,5,6),(1,3,5)] and B =  [(1,4),(3,6),(3,6),(2,6)] is given by:

ijth element in the product AB matrix = Summation of ( ij th element of A*ji th element of B)  j= 1 to 3.

Therefore A*B = [(4*1+5*3+6*2 , 4*4+5*6+6*6) , (1*1+3*3+5*2 , 1*4+3*6+5*6)].

A*B = [(31, 82), (21, 52)].