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.
Answer:
1.3, 2 1/3, 1.34 is the order from least to greatest
The path is in the shape of a parabola, the horizontal length is 24, so the middle point is at x=12, the symmetry line is x=12, the highest point (the vertex) is at (12,6)
the equation in vertex form is y=a(x-12)²+6
next, find a by using either one of the two points, the starting point (0,0) or the end point (0,24). obviously (0,0) is easier to calculate:
0=a(0-12)² +6
a=-1/24
so the quadratic equation is y=-
Rotation and translation are rigid transformations, they don't change figure sizes. Dilation change figure sizes increasing or decreasing them by scale factor.
First, find AB and A'B' by the formula:

As you can see AB=2A'B'. This means that the segment AB was decreased twice to form segment A'B'. Then the scale factor is 1/2.