Answer:
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.
4x^2 -28c + 40 = 1
-28c = 1 -4x^2 -40
-28c = -39 -4x^2
c = 39/28 + 4/28x^2
c = 39/28 + 1/7x^2 => answer
Hello,
since sin 30°=1/2 and cos 30°=√3/2
then
8(cos 30+i sin 30°)=8*(√3/2+i/2)=4√3+4i
Answer: B. -138
Step-by-step explanation:
For Negative numbers, the largest number is the least. I. This case, -138 is the least.
Hope it helps!
