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}

lwfrgin 2021-02-05 Answered
Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. A=[1234],B=[1234]
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Dora
Answered 2021-02-06 Author has 98 answers
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]
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2022-01-14 Author has 2047 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more