Check the true statements below:

a. A single vector by itself is linearly dependent.
b. If H= Span{b1,bp}, then {b1,...bp} is a basis for H.
c. The columns of an invertible n \times n matrix form a basis for R^n.
d. In some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix.
e. A basis is a spanning set that is as large as possible.

a) False

b) False

c) True

d) False

e) False

Step-by-step explanation:

a. A single vector by itself is linearly dependent. False

If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.

b. If H= Span{b1,bp}, then {b1,...bp} is a basis for H. False

A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.

c. The columns of an invertible n × n matrix form a basis for Rⁿ. True

If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.

d.  In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False

Row operations can not affect linear dependence among the columns of a matrix.

e. A basis is a spanning set that is as large as possible. False

A basis is not a large spanning set. A basis is the smallest spanning set.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

b mark me branliest thx

step-by-step explanation: