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A few things wrong over here, let's get started:Also just working on another question, especially stuck with the last part.
It's basically definitions.
View attachment 825
This is what i've got so far, correct me if I'm wrong.
Remember how matrix multiplication works: the number of columns of the matrix on the left has to match the number of rows of the matrix on the right. In this case, A has d rows, which means that x (a column vector) has to have d components. The product, b, will have the same number of columns as x (one column) and the same number of rows as A (k rows). So, b has k components.a) k components, k components.
I don't see an "n" anywhere in this question. Since A takes a vector of d components and gives a vector of k components, A is a map from $\mathbb{R}^d$ to $\mathbb{R}^k$.b) R^n to R^n
The answers to c) and d) are $\mathbb{R}^k$ and $\mathbb{R}^d$ respectively.c) R^rank(T)
d)R^nullity(T)
e) Completely unsure (need help with this)