Chapter 8.1, Problem 11E

To determine

To mark:

(a). The given statement, “The set of all affine combination of points in a set S is called the affine hull of S” as true or false.

(b). The given statement, “if $\left\{b_1,\dots ,b_k\right\}$ is a linearly independent subset of ${ℝ}^n$ and if p is a linear combination of $b_1,\dots ,b_k$, then p is an affine combination of $b_1,\dots ,b_k$” as true or false.

(c) The given statement,“The affine hull of two distinct points is called a line” as true or false.

(d) The given statement, “A flat is a subspace” as true or false.

(e) The given statement, “A plan in ${ℝ}^3$ is a hyper plane” as true or false.