Question

12 13 12 31 32 33 a31 a32 a33 a34 1 42 43 Denote row i in matrix A above as vector ai and row i in matrix B as vector bi; for example, a'-a a,, az, a24]. Similarly, denote column k in matrix A as vector ak and column k in matrix B as vector bk a) Does matrix C = AB exist? If no, explain why not. If yes, write it out expressing each element cik as the inner product of the relevant vectors defined above b) Does matrix D- BA exist? If no, explain why not. If yes, write it out expressing each element dik as the inner product of the relevant vectors defined above

Answer 1

a) Here the number of columns of A = 4 and the number of rows of B = 4.

Since the number of columns of A is equal to the number of rows of B, therefore the matrix C = AB exists.

Now, expresion for the product matrix C = AB is :

where i = 1,2,3 and k = 1,2,3.

b) Here the number of columns of B = 3 and the number of rows of A = 3.

Since the number of columns of B is equal to the number of rows of A, therefore the matrix D = BA exists.

Now, expresion for the product matrix D = BA is :

where i = 1,2,3,4 and k = 1,2,3,4.

Here the number of columns of A = 4 and the number of rows of B = 4. Since the number of columns of A is equal to the number of rows of B, therefore the matrix C = AB exists. Now, expresion for the product matrix C = AB is: where i = 1, 2, 3 and k = 1, 2, 3. b) Here the number of columns of B = 3 and the number of rows of A = 3. Since the number of columns of B is equal to the number of rows of A, therefore the matrix D = BA exists. Now, expresion for the product matrix D = BA is: d_ik = sigma_j = 1^3 b_ij a_jk where i = 1,2,3,4 and k = 1,2,3,4.

Thank you...