Multiplication of two matrices refers to the composition of two linear transformations. But, when

uto2rimxrs50

uto2rimxrs50

Answered question

2022-05-14

Multiplication of two matrices refers to the composition of two linear transformations.
But, when we look at a matrix representation of systems of equations,
  A x = b
where A is a m×n matrix, x is n × 1 matrix of n variables, and b is m × 1 matrix. We apply matrix multiplication here, but we don't refer this to the composition of linear transformations since it is a representation of systems of equations.

Answer & Explanation

Lilia Randall

Lilia Randall

Beginner2022-05-15Added 14 answers

If A is the matrix of a linear map L : V W with respect to two bases B and B and if the coordinates of a vector v with respect to the bases B are a 1 , , a n (that is, if v = a 1 v 1 + + a n v n , with B = { v 1 , , v n }), then the coordinates of L ( v ) with respect to the basis B are precisely the entries of the vector
B . [ a 1 a 2 a n ]
So, multiplication of a matrix by a vector corresponds to computing the image of an element of V. And therefore, solving an equation w = L ( v ) corresponds to a system of equations such as the one that you described.
Ashley Fritz

Ashley Fritz

Beginner2022-05-16Added 5 answers

I had the same problem, thanks!

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