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

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°