• We have a matrix which is a bunch of vectors together, where each vector is a column of the matrix.
  • Then we have the solution vector x which is a bunch of xs for each dimension collected together.
  • The matrix-vector product is the sum of products between the corresponding column vector and x in that dimension.
  • is a linear combination of elements of and columns of .

Alternative way to think of this

Row dot Column.

  • The row of the resultant matrix is a dot product between the row of the matrix and the vector .
  • Has just one column as dot product of vector sums up the product of the corresponding entries.