Step-by-step explanation:
Multiply the previous value by 3
Answer:
A, B, C
Step-by-step explanation:
Step 1: "AB ≅ DE, AC ≅ DF, and ∠A ≅ ∠D"
A. Given.
This is the information that was given in the problem statement.
Step 2: "ΔABC ≅ ΔDEF"
B. Side-Angle-Side Postulate (SAS)
The SAS postulate says that if two triangles have a pair of congruent angles between two pairs of congruent sides, then the triangles must be congruent. From the previous step, we can conclude the triangles are congruent.
Step 3: "∠C ≅ ∠F"
C. Corresponding parts of congruent triangles are congruent (CPCTC)
In Step 2, we established the triangles are congruent. So now we can conclude that the corresponding angles are congruent.
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.
