Compute AB and BA, which ever exists when A = [(1,2,3,4)] B = [(1,2,3,4)]

Question

Compute AB and BA, which ever exists when

A = [1 2 3 4] and B = \(\begin{bmatrix} 1 \\[0.3em] 2 \\[0.3em] 3 \\4 \end{bmatrix}\)

A = [(1,2,3,4)]

B = [(1,2,3,4)]

Answer 1

Given :  A = [1 2 3 4] and B = \(\begin{bmatrix} 1 \\[0.3em] 2 \\[0.3em] 3 \\4 \end{bmatrix}\)

Matrix A is of order 1 x 4 and Matrix B is of order 4 x 1

To find : matrices AB and BA

Formula used :

Where c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

If A is a matrix of order a x b and B is a matrix of order c x d ,

then matrix AB exists and is of order a x d ,if and only if b = c

If A is a matrix of order a b and B is a matrix of order c x d ,

then matrix BA exists and is of order c x b , if and only if d = a

For matrix AB, a = 1,b = 4,c = 4,d = 1 ,matrix AB exists and is of order 1 x 1, as

b = c = 4

Matrix AB = [1 + 4 + 9 + 16] = [30]

Matrix AB = [30]

Matrix AB = [30]

For matrix BA, a = 1,b = 4,c = 4,d = 1 ,matrix BA exists and is of order 4 x 4, as d = a = 1