00:01
In this question, t is a linear transformation from rn to rm, defined by the formula t of v equals to av.
00:08
We are asked to find the dimensions of the numbers n and m, where a is the given matrix.
00:15
Now, let v be some vector, and t of v equals to the matrix a multiplied by the vector v, right? now, what should be the dimensions of the vector v in order for this multiplicity? to be defined.
00:38
We are multiplying 1 by 4 matrix, which means 1 row and 4 columns matrix by some vector.
00:46
For the multiplication to be defined, the number of entries in the vector should be equal to the number of columns of the matrix 8.
00:56
So, v should be a 4 dimensional vector, v1, v2, v3, and v4.
01:05
This means that the dimension of rn should be equal to 4, because we are applying our transformation to a four -dimensional vector.
01:17
That's a domain.
01:18
V is in the domain, and the domain must be four -dimensional...