The top one is the answer
X=k*Y
K*Y=X
K=X/Y
K=20/5
K=4
For Y=3/2
X=k*3/2
X=4*3/2
X=6
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:
Step-by-step explanation:
2x + 3y = 2
x = 2 - 3y /2
x + y = 0
substitute the value of x
+ y = 0
2 - 3y + 2y = 0
2 = y
again,substitute the value of y
x = 2 - 3y / 2
=2 - 3*2 / 2
=2 - 6 / 2
=-2
X3-7x=6x-12
x3-7x-6x+12=0
x3-13x+12=0
(x-1)(x2+x-12)=0
Calculate delta of the second bracket:
delta = 1+4*12=49
sqrt(delta)=sqrt(49)=7
x_1=(-1-7)/2=-4
x_2=(-1+7)/2=3
(x-1)(x+4)(x-3)=0
Answear:
Roots: x=1, x=-4, x=3.