Determine whether the following statements are True or False.

a. The columns of an invertible n×nn×n matrix form a basis for RnRn.
b. If H=span{v1,...,vp}H=span{v1,...,vp}, then {v1,...,vp}{v1,...,vp} is a basis for HH
c. A single nonzero vector by itself is linearly dependent.
d. A basis is a spanning set that is as large as possible.

Step-by-step explanation:

a.  True

b.  False

c. True

d. False. when its too large then it can no longer be linearly dependent

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

roots are from trees

step-by-step explanation: