Q6Multiple correct3 Marks22 Dec 2024

Assume the usual vector addition and scalar multiplication for all the options below. Choose the correct option(s) from the following statements.

A

The set of vectors {(x, y) in $\mathbb{R}^2$ | x + y = 1} forms a vector space.

B

Let A in M_{3x3}(R) be a matrix such that the columns of A are linearly independent. The set of all solutions of the homogeneous system Ax = 0 is a vector space of dimension 0.

C

The set of all n x n matrices with rank strictly less than n does not form a vector space.

D

The set of all n x n matrices with determinant 0 forms a vector space.