Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. A=[1234],B=[1234]

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Dora · Accepted Answer

Step 1  the given matrices are:  A=[1234],B=[1234]  we have to find (if possible) the matrices:  (a)AB  (b)BA  Step 2  as we know the product of the two matrices is possible if the former matrix in the product has no. of columns equal to the number of rows of the latter matrix.  for example if  we have two matrices A and B having orders m×n and p×q respectively then for product AB to be defined the number of columns of matrix A should be equal to the number of rows of matrix B that implies n=p and for product BA to be defined the number of columns of matrix B should be equal to the number of rows of matrix A that implies q=m therefore as the given matrices are:  A=[1234] and B=[1234]  matrix A has order 1×4, that implies matrix A has 1 row and 4 columns.  matrix B has order 4×1, that implies matrix B has 4 rows and 1 column.  Step 3  now as no. of columns of matrix A is equal to number of rows of matrix B.  therefore the product AB is defined.  therefore,AB=[1234][1234]  =[1×12×23×34×4]  =[14916]  [30]  therefore, AB=[30]  Step 4  now as number of columns of matrix B is equal to number of rows of matrix A. therefore the product BA is defined.  therefore, BA=[1234][1234]  =[1×11×21×31×42×12×22×32×43×13×23×33×44×14×24×34×4]  =[1234246836912481216]  therefore, BA=[1234246836912481216]

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. A=begin{bmatrix}1 & 2 &3&4end{bmatrix} , B=begin{bmatrix}1 2 3 4 end{bmatrix}

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