Question

Construct a 4 × 얹 matrix A-I a, a2 a3 1 such that {a, a2Hs a linearly independent set and als not in the span of [a,,a2

Answer 1

To construct a 4 x 3 matrix with a linearly independent set and not in the span of [a, a^2], you can set up a matrix with the given conditions.

Step-by-step explanation:

In order to construct a 4 x 3 matrix where {a, a^2, a^3, 1} is a linearly independent set and not in the span of [a, a^2], we can set up the following matrix:

aa^2a^31100001000010

This matrix satisfies the given conditions because the first row represents the elements {a, a^2, a^3, 1}, which is a linearly independent set, and the second and third row represent the elements [a, a^2], which is not in the span of [a, a^2].