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:
24/40 = 4/5
18/42 = 3/7
Step-by-step explanation:
Sana makatulong
Answer:
True
Step-by-step explanation:
A new shape with an area of 1 square unit that is not a square can be formed by combining two small triangles
<h3>How to determine the new shape?</h3>
The given parameters are:
- Area of square = 1 square unit
- Large triangles = 2
- Medium triangles = 1
- Small triangles = 4
The area of each small triangle is:
Area = 0.5 square unit
Multiply both sides by 2
2 * Area of triangle = 1 square unit
Substitute Area of square = 1 square unit
2 * Area of triangle = Area of square
This means that a new shape can be formed by combining two small triangles
Read more about area at:
brainly.com/question/24487155
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You could sort them by there sides. So you count how many sides the figure has. Then it would be split up by two groups. One with with 4 sides and 1 with 3 sides.
