Answer:
Step-by-step explanation:
(5,7) and (7,-3)
m=(-3-7)/(7-5) = -10/2 = -5
Equation of a line is
y-y1 =m(x-x1)
y-6 = -5(x-5)
y = -5x +25+6
y = -5x +31
Hi
Here is the Justification
Line 1 : 3p-(p+8) = 5p-7 [Given]
Line 2: 3p-p-8=5p-7 [ Applying distributive property]
Line 3: 2p-8=5p-7 [Simplifying like terms]
Line 4: -8=3p-7 [Subtraction property]
Line 5 -1=3p [Additive property](Add 7 on both sides]
Line 6 -1/3=p [Multiplicative inverse or division]
Line 7 p=-1/3 [Property of equality]
Thank you.
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.
I do believe the answer is m<30
