Check the statements below that are true The columns of an i

Check the statements below that are true. The columns of an invertible n X n matrix form a basis for A single vector by itself is linearly dependent. A basis is a spanning set that is as large as possible. If V = span{v_1, v_2, ..., vp}, then {v_1,v_2, ..., vp} is a basis for V. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix.

Solution

A. The columns of an invertible nxn matrix form a basis for Rⁿ . TRUE They are linearly independent and span Rⁿ.

B. A single vector by itself is linearly dependent. A single vector is itself linearly dependent. FALSE unless it is the zero vector.

C. A basis is a spanning set that is as large as possible. FALSE .If it is too large, then it may no longer be linearly independent.

D. If V = span { v₁ , v₂,…, v_p} , then { v₁ , v₂,…, v_p} is a basis for V. FALSE They may not be linearly independent.
E. In some case, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations upon the matrix.. FALSE These are not affected